Alright, all set. Because I don't like to do things half-assed, there's a description for each MU to help get my point across, as well as to allow people to more easily rebuke what I've said and offer their own opinions. Before even starting the list, though, it's probably best to mention what I see as +'s when it comes to Zack, so you can consider them when pondering the MU.
Zack's +'s :
Extremely powerful
Long delayable strings
Decent tracking
i11mid with follow up
6T punish throw with guaranteed followup and 50/50
Plenty of fast lows, some of which are a start to strings
Great at creating space
Good at maintaining space
Good at closing space
Extremely high wall damage
Powerful throws for a striker
Access to a throw which, if not broken, guarantees a stun
Great mixup potential
Safe/numerous stance transitions
2 CBs, mid kick and mid punch.
CB combo damage rivals his PL damage
Decent amount of safety
Easy access to +frames on block
Akira - (5-5) There's not much to be said of this matchup, really. Neither has any real edge over the other.
Alpha152 - (6-4) She may have an i9 jab, but that's not as crucial as having an i11 mid, which she lacks. And while she may have insanely long strings and string delay, Zack is right up there with here. He has both the offensive and defensive tools to make this matchup a difficult one for her, as he's pretty good at spacing, great at close-up confrontations, and can be fairly evasive with his Duck SS to evade her linear hits.
Ayane - (5-5) Ayane may be the queen of spacing, but Zack, when push comes to shove, can create and hold distance fairly well himself. He also has very safe/far reaching attacks to get back into range should the need arise. He also has one benefit that a lot of the cast is missing, and that's being able to (with quick enough reflexes) get 100+ damage guaranteed should Ayane ever try to use 66KK4, severely limiting her own tools for closing the gap. She has her roll obviously, but 4K can easily shut it out, and his Duck SS can evade most every other option of hers at a distance. When it comes to close quarters combat, she's more crush-heavy, but Zack is more powerful and has the better mixup. And while she has a better throw for most situations (64T), Zack has the better punish throw in 6T. This may wind up leaning more towards Ayane, but her tools aren't as effective against Zack as they are with some of the rest of the cast.
Bass - (5-5 or 6-4) Bass can be an annoyance, but in the end, he's another fairly even matchup (though perhaps even in Zack's favor). Bass, obviously, can punish otherwise safe strings/pokes, and he also gains frame advantage afterwords. He also has powerful mid counters, which are Zack's best tools, as well as 3K which can really hurt Zack's Duck stance, as he gets a lot of free damage from the SDS. Add into consideration that most every launch of his will end up with the opponent on their feet with Bass at +frames, and he's really quite a pain. He's also a heavyweight, so a lot of combos do not work on him, and weight affects Zack more than the rest of the cast due to his odd combos. All of that said, Zack can be a pain in the ass for Bass as well. His speed, coupled with his constant onslaught of attacks and a crushing stance help him to keep Bass at bay. What's more, Zack's spacing can completely halt Bass' advances due his lack of tools to close gaps as well as (in most situations) lacking the range that Zack possesses. The problems each one causes the other balance out the MU in my opinion, though again, I can see it leaning in Zack's favor.
Bayman - (4-6) One of the few uphill battles. Bayman's parry can shut down most of Zack's mixup, and once again, weight plays a large factor in limiting Zack's combo potential. This MU may be 5-5, but the Tank Roll coupled with Bayman's parries/extremely powerful counters and OHs can be problematic if you're playing against someone who knows how to use them effectively.
Brad - (6-4) Brad is great against characters with short strings with a focus on mids/highs, but he's not too great when playing Zack, is mostly because Zack has so many lows in his strings, as well as long, re-tracking strings and mid-string tracking hits. If Zack can hit Brad's back (in just the same way as Ayane), he can get a lot of free damage with unshakeable combos. He can also hit a lying down Brad fairly safely and create a nice gap between Brad and himself with most of his counters. There's no real advantage that Brad has in this MU, which is why I'm calling it in Zack's favor.
Christie - (5-5) As previously mentioned, Zack has long, re-tracking strings as well as some fairly decent tracking in general. Now, Christie has a superior crouching SS of course, but Zack's damage far outclasses her own, whether when out in the open or by a wall. It also helps that he can Duck SS quite a few of her mixups. She obviously outspeeds Zack, which can be an issue, but they're tied in mid speed, so the only thing she's faster in is her i9 jab. Her lack of low stuns coupled with the nerfs to JAK and Zack's fantastic mids help to mitigate most issues she usually causes opponents.
Eliot - (6-4) Eliot doesn't have many great MUs, and I'm not sure if that's due to being underused or being misunderstood, but there's not much Eliot has going for him in this MU. Both characters have long strings, the same speed (relatively speaking), powerful wall combos, and powerful open-air combos. Zack has a formidable spacing game, a crouching SS, plenty of stance transitions, easy access to frame advantage, one of the best punish throws in the game, and an exceptionally high damage output off of CB. Eliot has his parry (which, let's be honest, is outshined by Bayman's and Gen's), an i9 high, and a fairly powerful air throw. Zack can crush Eliot a lot mid-string, which severely limits Eliot's options in a match as well.
Gen Fu - (4-6) This is likely the MU for most characters against Gen. Right off the bat, Gen's parry is severely problematic, granting him a free stun and 50/50 while also nullifying Zack's mid mixups. He has a lot of crushes to deal with Zack's highs as well, plus linking SDSs for lots of free damage. Gen can also negate wakeup kicks far more easily than Zack in addition to racking up damage quicker as well. There's little Zack has going for him in this MU other than his decent spacing and crouching SS, but that's really it.
Hayate - Unknown. Hayate is a character I hardly understand. I don't know his strengths or weaknesses, and I don't want to speak out of my ass when talking about this MU. I'll just say that I feel safe fighting him with Zack, though not overly powerful, so as a complete guess, I'd wager 5-5. I'd like some help from Hayate players, though, for more input.
Helena - (5-5) Helena can be annoying. Her 33P crushes a LOT of Zack's mids, including his 6P (which is arguably his best mid). She also has a dangerous mixup game that surpasses Zack's. Her throws are either powerful or grant her frame advantage and 50/50s, and she has plenty of safe, long reaching lows. Zack, on the other hand, doesn't need to spend as much time as she does hitting people for a CB. Hell, he doesn't even need to go for the CB for decent damage. While her throws are good, his 6T outclasses most of them, along with his wall throws and other throws that either utilize electrified floors, create distance, or provide him with a free 50/50 as well (Duck T). His strings are long, so her BKO duck don't prove too useful, plus he has plenty of lows to hit her regardless. 4K also causes a SDS when used on crouching opponents, so that helps to lessen the fear of her BKO stance.
Hitomi - (5-5 or 6-4) While Hitomi in general is dangerous online, that all changes with the lag gone. Her punch parry and poweful mid-kick hold may prove frightening, but her general lack of mid tracking and fairly predictable kicks make it a fairly split matchup. There's not much to say here, really, other than they both have decent 6T's (though Zack's is the better of the two), they both have fairly long, delayable strings, and they both have fairly annoying lows.
Jann - Unknown. Once again, I'm not too familiar with Jann to speak about this MU too much. Obviously, he has the Dragon Gunner, fast mids, great spacing, and a high damage output, but I'd still rather not comment on this. I'd say it leans more in Jann's favor, but I could see a potential 5-5.
Kasumi - (5-5) If it weren't for Kasumi's speed, this would easily fall into Zack's favor. They both have great wall damage, and while Kasumi has superior pokes and speed, Zack has superior mixup and crushing capabilities. Zack can play a decent spacing game, but Kasumi can close the gap quite easily (so long as she judges the distance for a 3P+K appropriately, or else she'll eat a 4K). Kasumi does have more guaranteed damage than Zack does, but again, his crushes and mixup can hurt Kasumi quite easily.
Kokoro - (6-4) Much of the reason why this is 6-4 is because of Kokoro's linearity. She already has enough problems playing people with normal SS, but add onto that Zack's crouching SS, and she because a lot easier to deal with. Kokoro has a lot of things going for her. Throws from strings, high damage, decent mixup, 2 powerful launches, decent throws, and a decent stance. Zack has all of that plus a greater mixup factor, better tracking, longer strings, better throws, spacing tools, a decent amout of crushes, and that coolness factor. Can't forget his coolness factor.
Leifang - (5-5) In this case, she's just a less dangerous Bayman. Most of the time, Leifang is a more solid choice, but I have more issues against Bayman with Zack than I do against Lei. Now, this may be just a personal issue, but Lei can be fairly unsafe, and Zack has great throws in general plus one of the best punish throws in the game. Her slew of parries aren't too terrifying, as one grants her very little damage, while the other just grants her one free hit into a 50/50. Now, her mid-kick counter (advanced or otherwise) is an absolute nightmare for Zack, but just as she gets a large chunk of damage for that particular counter, Zack can get off just as much with some of his throws should he be expecting it. Now I know that can be said about the others as well, but Leifang is really just a very solid, well-rounded character with no really damaging flaws; she's not particularly threatening to a lot of the characters, just as much of the cast aren't very threatening to her.
Lisa - (6-4) Lisa doesn't have much going for her in this MU. She can be tricky with her throws/CB setups, but Zack can as well. Both have access to both a mid punch and mid kick CB, and both are decent at spacing/closing gaps. What Lisa lacks is the mixup that Zack offers, plus the general range of her strings and a punish throw that pales in comparison to Zack's. Zack also has the higher damage output, better crushes, better SS along with general SS options, and slightly better tracking, though her 1K is certainly a powerful tool. Lisa also comes equipped with OHs, something Zack is lacking, as well as powerful 3 part throws, one of which being unbreakable. Again, though, Zack has the superior punish throw which matters A LOT, as well as generally powerful/useful throws in general. Basically, it comes down to what does one have that the other doesn't? Lisa isn't a terrible character by any means, but none of her strengths really prove too useful against Zack.
Mila - (4-6) Until they remove the ground throw/low throw option select for the characters that have low throws, this will be in Mila's favor. As it stands, she can use any launch to gain either a ton of damage or eliminate WUKs and be at +5-ish while doing so. Add onto that her punish throw being as good as Zack's, plus having OHs, power to match Zack's, general safety, decent mixup, and a counter-deterrent in the form of 7K, and there's not much Zack (or most characters, for that matter), can do.
Pai - (5-5) It's difficult for any character to hit Pai, and that's even more problematic for characters lacking an i9. She outclasses him in speed and frames, as well as mix-up. Her throws are also frightening, though Zack's 6T is far better than her own. She's also very adept at crushing with 7H+K, 33P, 2P+K, and her low sweeps/jab, so it can be difficult to get a hit in on her. That said, while she's far more terrifying up close than Zack is, she has a pitiful spacing/range game, and has extreme difficulties closing gaps created by opponents. As Zack can make gaps extremely quickly as well as close them quite efficiently, she needs to be in the entire time with throw mixups and resets to hold her own. As I mentioned on an old status, she needs to make a lot more correct guesses than Zack does to get the win, but she's lucky in that the correct guess usually leads into a respectable amount of guaranteed damage, as she has some threatening 50/50s as well as easy access to great SDSs.
Rig - Unknown. Rig is the one character I still don't know how to play as. And since I don't even know how to use him on any level, I have less of an idea on how to fight him. While I'd like to say it's 5-5, I honestly think it's shifted more in Rig's favor due to Rig's constant frame advantage, powerful launching throw, access to easy ceiling combos and SDSs, as well as great mixup.
Ryu - (5-5). Ryu can be a little intimidating, though I'm not sure that's enough to warrant him having a superior MU against Zack. Yes, he's a grappler with fast/powerful throws much better than Zack's, and he has fairly decent speed to match Zack's as well. Ryu also has better frame advantage on block with several moves, and can easily abuse ceilings/ledges/counters in general. Having said all of that, Zack doesn't really care too much. Ryu has great throw damage, but Zack his amazing combo damage. Zack also has a much easier time getting stuns/hits to start juggles than Ryu, and while his throws aren't as powerful, they can be just as difficult to deal with considering the 50/50 that follows 6T or the free stun that follows Duck T. Zack's spacing doesn't help much in this MU as Ryu can instantly close it with a teleport (as risky as they can be) or quickly get in through other means.
Sarah - (5-5 or 4-6) Sarah is a thorn in everyone's side. She obviously has the superior mixup along with deeper stuns, attack grabs that work on both hit and block, VF frames, and a fairly potent juggling capability. Zack's tools don't really function too well against her (apart from spacing), and he's usually beaten out when trying to hit her.
Tina - (6-4) Tina is a faster version of Bass, but without all of the delicious + frames. She's not too great at crushing (though 1P can be annoying), her speed is subpar, and she also does less combo damage than Zack. What she does have going for her are fast tracking moves (1P, 4P), extremely powerful throws, OHs, and a few guaranteed hits. Though needless to say, it doesn't really compensate for what she lacks, and Zack isn't really lacking in any category. So long as Zack doesn't try to counter too often, Tina's damage won't outpace his own in most circumstances.
Ein - (6-4) Ein is meant to be played defensively, or so most everyone says (myself included). He has a really solid spacing game, but so does Zack, which is why it's not doing Ein many favors. Ein can keep people at bay, that's a fact. But when it comes to getting back in if he's at a health disadvantage, he's outclassed by Zack. Now Ein can play keep-away better than Zack, but with the range/safety/tracking on some of his ranged tools, Zack doesn't have a huge issue getting back in if the need arises. When Ein's one strongpoint is only mildly better than Zack's, it becomes an issue for him. So while Ein does edge Zack out in spacing, he loses in getting back in, damage output, mixup, frames and (perhaps) throws. Ein's 33T is obviously amazing, especially against walls, but that requires a counter for huge damage whereas 6T from Zack just needs to be thrown out whenever, getting him 55 on NH in addition to a tricky 50/50.
Jacky - (5-5) I'm honestly not sure about this MU, but it's pretty close to even in my opinion. Both have great mixup, powerful throws, high damage output, decent lows, decent tracking, and have similar speed. Zack has the better mids, but Jacky has access to better frames. And while Zack could forego stuns and head straight into a launch, he doesn't get as much damage from that as Jacky does. But again, Zack's spacing game help keep him afloat in the matchup.
Leon - (4-6) I'm reluctant to give this a 4-6, as it could easily be 5-5 or even 6-4, but Leon is a simply terrifying character. 3K, in much the same way as Bass, helps to shut down Zack's ducking moves. Leon also has decent tools for opponents at a distance, either using his running P with plenty of active frames/range/guard break, or going for his running T that crushes/tracks/devours hits. Add onto that his 33P > 8PP mixup, his extremely powerful throws, general guarantees, and ability to completely bypass stuns and head straight for a launch, and he's really difficult for Zack to deal with. Once again, being a heavyweight, Zack's damage is scaled down a lot. And while Leon doesn't have much tracking, his throws and frames (and occasionally useful lows) bypass that flaw fairly well. Zack obviously outpaces him and has the superior mixup, but Leon doesn't really need that to get a win or to get damage.
Momiji - (6-4) Momiji is simply annoying. She has decent mixup, but it's not as good as Zack's. Her best options are from the air, and Zack can use his Duck 2/8 to get out of them all so long as he's not in stun. I can't recall, but I don't think she has an i11 mid, so in terms of speed, she's beaten out by Zack. She's a fairly mediocre character (tool-wise) and doesn't really measure up to Zack's capabilities. Sure, she can get decent damage from a stun > launch, moreso than Zack probably, but in most every other regard, Zack outright trumps Momiji or has the tools to answer her own.
Rachel - Unknown. Now, this isn't because I don't know Rachel or what she's good at. It's simply because I don't know how I feel on the matter. I almost never fight Rachel when using Zack, so I'm not sure what works against her, what doesn't, what can be used to stop something of hers, etc.