Leadership

Currently tameable critters include:

Deer (you need to damage them a little to get them to come close enough!)(level 3?)
Sheep (level 3?)
Cows (level 4?)
Dogs (level 5?)
Grass Vipers (level 5)
Cats? (not sure if they're still tameable or not)
Wolves (level 12)
Bear Cubs (level 14)
Stags (level 20)

With the Demon Spire update, the maximum number of pets tameable regardless of skill level is 3.