/warp Zoo will soon contain every mob that can be transported and contained in vanilla Minecraft.
Without spawning in any mobs.
Here's how it's been done, in order of appearence in the zoo:
Snow Golem - created on the spot
Wolf - native to the surrounding forest. They are easy to push into boats, which can then be driven by a player.
White and Black / White Rabbits - native to ice plains 2500 blocks away, as the crow flies. They were picked up with leads and flown this distance.
Polar Bear - same as above
Stray - transported via boat as leads do not work on hostiles ~7500 blocks
Cave Spider - transported via stairs from a mineshaft under the zoo
Spider - spawns in darkness
Creeper - spawns in darkness
Zombie - spawns in darkness
Villager - transported via boat and river from a nearby river
Iron Golem - created on the spot
Cow - spawns on grass
Sheep - spawns on grass
Horse - spawns in plains
Donkey - spawns in plains
Mule - bred from above two
Pig - spawns on grass
Chicken - spawns on grass
Husk - transported via boat/river/tunnel from desert
Yellow Rabbit - transported via lead and flight
Skeleton - spawns in darkness
Skeleton horse - spawns when horses are struck by lightning; these bolts do not follow storm patterns and are common if you are near lots of horses.
Magma cube - spawns in nether; transported via portal
Zombie Pigman - see above
Blaze - spawns in fortress; transported via boat and portal
Wither Skeleton - see above