Strength in numbers: This one's obvious by now, but you need to be with other zombies to really do any damage. You can convert NPCs, but not very quickly unless they're low level, and low level zombies drop relatively fast. It's far better to convert players (usually by listening in for anyone who wants to be a zombie, and then inviting them to a zombie party off the beaten path). But the key is to wait until you've got a good group -- any zombies that go shambling off by themselves are going to get quickly overtaken by NPC guards or overzealous Paladins.
More tips after the break.
Communicate! Normal zombies can't do much more than mumble and murmur the occasional "braiinnnsss!" but we player zombies can talk all we want to each other. Use that -- communicate with the zombies you come across in the world, and even coordinate attacks in, say, a "Zombies" chat channel (type "/join zombies" to see if someone's formed one on your server). Keep the information flowing, and when the enemy attacks one flank, cue fellow zombies to circle around to the other.
Eat or die: As you've noticed, zombies will lose health after a while, but the good news is that they can gain it by attacking. And you can gain it by attacking anything, humanoid or otherwise, so if you need to make a long trip as a zombie, you can periodically eat mobs on the way to stay alive. And if you happen to come across a humanoid settlement or unguarded guard tower on the way, well, it's buffet time!
Spread the plague: As you've noticed from our gallery, there's no reason you shouldn't have the Retch! AoE running whenever possible -- it slows down your prey and keeps you healed. Use it as a quick snare if your meal is running away from you, throw it down to heal yourself when you're in the middle of a trip and need to keep your health up, and make sure it's down whenever you're attacking anything -- with the health you get back from attacking plus the Retch bonus, you can take down pretty much any single target. And with enough zombies, even those righteous Paladins who think it's funny to cleanse the plague off and kill that which has already died can even meet their maker. Which, since they'll become a zombie themselves, is you.
Lurchin' around: And speaking of using your abilities, if you are in a group, don't all hit your Lurch at the same time and waste it. If you're chasing down a target as a group and you're already Lurching forward, wait until the buff drops, and then hit yours. It only last 10 seconds, but there's a 30 second cooldown, so a well-coordinated group of 3 zombies can basically Lurch indefinitely if they keep the buff rolling.
Slow and Steady: Lurch aside, Zombies didn't take over the world by sprinting around (well, ok, they did in 28 Days Later, but that was some biowarfare thing, not the actual undead). They took over the world by shambling about, slowly and carefully. So don't just run in as a group of five or six to a major capital city, and expect to topple it -- start simple, in Lakeshire, Westfall, Razor Hill, or Crossroads, and recruit fellow zombies to your cause. Once you've got a nice group (again, communication is the key), then you can start to make your way to bigger settlements like Stormwind and Orgrimmar. And if the lousy Paladins overtake you there, too, don't worry -- from everything we've heard, they'll get their day of the dead soon enough.
Any other good tips you've discovered for keeping the plague spreading around the world? One of us!