Rabbits

Rabbits, also known as hares, or conies by Hobbits, were small, fat animals which lived throughout Middle-earth. Rabbits were hunted for food by the peoples of Middle-earth, usually when traveling and not as butchers cuts, save for the Beornings who did not eat meat.
Radagast's sled is pulled by a strange, large breed of rabbits from Rhosgobel, called "Rhosgobel Rabbits" by the wizard, which were fast enough to outrun Wolves from Gundabad and also Wargs.
A brace of rabbits were caught by Gollum just before a force of Haradrim walked through the land with an Oliphaunt, but then are then cooked by Sam in a stew, which angered Gollum.