NOTE: As of version 3.1 animals can no longer be tamed.
Each animals have their own favorite food. Try to find them and drop on their heads. After a dropping a few, they will be tamed and their name is "label". You can press M on them to change their name.You can ride them, too (riding animals tend to be very hard, but rewarding, and requires good timing and practice). Tamed animals need to be fed from time to time. If they are not fed, they will die.
Gazelles/Reindeer: Flax [60 speed when riding]
Ostriches: Flax [60 Speed when riding]
Bears/Polar Bears: Raw Human Flesh [X speed when riding]
Rhinos: Raw Human Flesh [X speed when riding]
Hippos: Watermelon [15? speed when riding]
Turtles: Guppy [X speed when riding]