I've got a few (anything not mentioned isn't even considered). In descending order:
Invoker (DnD 4th edition) would be one approach. AoE spells similar to a mage, but with a divine bent, so I'd have a good amount of anti-undead stuff too.
Avenger (Again, DnD 4th edition) would probably be what I would end up with. Rogue with divine abilities? Yes, please! Problem with this? Would require me getting into melee. Not too keen on that in a zombie apocalypse.
Necromancer (Any): Given the amount of undead based abilities that the Invoker and Avenger would have, I think this might not work quite as well as them. Either make the army of dead MY army of dead or, in the case of being overwhelmed, make the army of dead... a pile of ash.
Paladin (WoW): Gimmie a big ass blade, some armor, and let me go nuts. Shit will die.
Paladin (DnD 4th edition): A bit more resilient than the WoW version, I'd be able to actually both shield my group and dish out a decent amount of destruction. Also, since the "code" would depend on the chosen deity... gimmie a Paladin of Kelemvor, the God of the Dead (who hates undead more than any other). Shit's gonna 'splode.
Wizard (DnD 3.5 or 4th): Not too keen on the idea of having to spend a ridiculous amount of time studying in the middle of a zombie apocalypse with the ability to turn a horde of zombies into... a horde of flaming zombies.
Warrior (Any): There's something to be said for brute force wielded by someone who's been trained for years on end. This guy might be able to stand up to a zombie apocalypse for an extended period of time, but he's gonna run out of steam eventually.
Barbarian (DnD 3.5 or 4th): Nice hit potential, but, again, melee. Also the whole "rage" aspect would be relatively... detrimental.
Cleric (DnD 3.5): This class relied a little heavy on melee combat for my tastes... and I'd end up having to choose between keeping my ass alive or killing zombies. Probably gonna end up being the latter, which would end up getting myself killed. Skipped.
Warlock (DnD 3.5 or 4th): I escape the horde of zombies by... making a deal with the devil. Good plan.
Rogue (Any): The problem with being an assassin in a zombie apocalypse is that, despite all your training in killing a human, you can't really stab a zombie through the throat for much of an effect. Yes, you could cut tendons and such, but, given that the stuff doesn't technically work anyway, I'm hard pressed to believe that that would do anything.
Druid (DnD 3.5 or 4th): I run into a similar problem with this class as I would with Cleric or Wizard. Given that you'll have access to healing spells, you'll be awesome, and you have the ability to set the zombies on fire (see above) you might be able to do some real damage to the zombie horde. Unfortunately, your abilities are tied to the very nature that's being warped. Will you become a necromancer, or will you become a zombie yourself?
Spirit Shaman (DnD 4th): NO, NO, ABSOLUTELY NOT. Like a druid, you have your abilities tied to nature. Unlike a druid, your abilities are tied to the spirits of nature, which are likely going berserk at a time like this. YOU WILL NOT KEEP SANITY FOR LONG.
Sorcerer (DnD 3.5 or 4th): This class has a similar problem with spellcasting that the Spirit Shaman would: Your spells are tied to magic in and of itself. Unlike a Wizard, who can choose not to access magic, your magic is tied to your very blood. What happens when magic starts going nuts a-la zombies?