Oryctolagus cuniculus, also known as the European or common rabbit, is generally the species of rabbit people keep as pets. A rabbit's muscle mass is more than 50% of its body weight, with the skeleton only making up about 7-8%. They have a digestive system very similar to horses (both of which cannot vomit). Their jaws make about 120 movements a minute.
Males are called bucks, and females are called does. They are quite successful at reproducing. Baby rabbits are called kits. Do not disturb a mother and her newborns. She may end up cannibalizing the kits.
Behavior-wise, rabbits tend to be active and curious (and some can be escape artists). They move around by hopping and may stand on their hind legs sometimes. They tend to bolt or cower when frightened.
They can be messy...their feces (poop) are usually small round pellets. Their urine can be clear red or yellow or milky yellow (because they have a lot of minerals in their urine). They also produce another kind of feces, that their owners probably never see, called night feces. The rabbits eat this kind of feces to recycle protein, water, and B vitamins (appetizing, huh?).
Rabbits can be housed indoors or outdoors and can be trained to use a litter box. Where ever you house them, they need some type of hiding place so they can feel secure. They'll also need protection from predators and temperature extremes. If they get too hot, they will not increase their water intake, and they only sweat from their lips (they're pretty good at conserving water). When deprived of water, they also stop eating (one of the first signs of a sick rabbit is loss of appetite). They use their ears to help them cool off.
While rabbits can co-habit peacefully with other species (like Guinea pigs), it is not recommended because they can infect other animals (like Guinea pigs) with Bordetella bronchiseptica (one of the factors in the "kennel cough complex").
This information is from a lecture given by Lucy Senter, DVM at Missississippi State University College of Veterinary Medicine.