I'm a big fan of the all-black zombie deck.  Zombies historically have a wide variety of interesting abilities, allowing the zombie deck to be versatile and powerful, if notoriously slow.

This deck is not versatile, but it is a good bit closer to a more traditional idea of how the zombie apocalypse would happen.  Use Dream Twist and the Looters to start building your graveyard and get some early Zombies on the field.  Dig in.  Get comfy.  Let your Diregraf Ghouls take some punishment.  Play an Armored Skaab or Unbreathing Horde to shore up your defenses.  Skaab Ruinator can turn the tables if things aren't going your way, and having a Vengeful Pharaoh in the graveyard early will keep your opponent's offense from getting too powerful.  Besides, your Hordes only profit from the extra zombies in the graveyard, and you can always play the Grimoire to get everything back again.

It doesn't get good until your first Undead Alchemist hits the field.  Then all hell breaks loose.  Start laying into your opponent with Flashback Dream Twists and your fliers.  Swing with everything.  Let your opponent supply you with blockers as their deck dwindles down to nothing.  The road is long, but it's very rewarding to sit behind an army of 30+ 2/2 zombie tokens, most of which have been generated by your opponent's lost creatures.

As for sideboarding, Surgical Extraction is a no-brainer.  Mana Leak or Cancel is a good way to keep Day of Judgment from ruining your day.  Grimgrin's a fun card in theory but I find him a little unwieldy in practice.  Some of the bigger Skaabs can be nice, but the fliers can more consistently deal damage.  Reassembling Skeleton can help you in the early game, and as fodder for the Skaabs, but he isn't a Zombie, so he doesn't help the Hordes at all.