Pet rabbits can be quite readily kept in cages in the home, with some freedom to run free in the house (after thoroughly rabbit-proofing, of course). Rabbits take fairly well to litter training, so many people will let their bunnies run free in the home for at least part of the day. Even if your rabbit is thoroughly toilet trained and your house thoroughly rabbit proofed, a cage will act as a safe haven or nest, where the rabbit can retreat to rest.
There are a lot of cages sold for rabbits that aren't really ideal rabbit homes, though. Some are just too small, and many have wire floors, which may make cleaning easier but doesn't provide much comfort to the bunny.
As usual, bigger is better. If your bunny will spend most of its time in a cage, then get the biggest cage that is practical in the home. As a general rule, the cage should be at least 4 times the size of the rabbit. A guide is 24" by 36" for smaller rabbits (less than 8 lbs.) or 30" by 36" for larger rabbits. A two story condo with a ramp joining the levels seems popular with rabbits too.
As a rule, rabbits take fairly well to being litter trained, so a solid floor is fine and not too difficult to clean. Many cages meant for rabbits are still made with wire floors over pull out pans, designed to make cleaning easier. However, wire floors (even those with very narrow spacing) can be uncomfortable and can cause sores or the hocks, so it is best to get a cage without wire floors.
Wire floors should be covered with a piece of wood, or grass or sisal mats (grass mats are nice to have in solid floored cages too, to vary the surface and provide traction).
The door to the cage should be about large enough to get a litter pan (and rabbit) through easily. A side door is probably best, as a top-opening cage makes getting the rabbit in and out a little harder (and it is best if the rabbit can get in and out on its own).
The opening should have smooth edges, or plastic guard strips over the edges of the wires.
If you are handy, you can get fairly creative and construct your own cage. This allows a custom size to be designed. My own rabbit has a homemade cage that is not ideal but works fairly well.
Grass/sisal mats are a good idea for solid floored cages, too, to provide traction. Fleece blankets can also be provided. Pieces of carpet or towels also make nice mats, as long as your rabbit is not unravelling and eating them.
As for other pets, cedar and pine shavings should be avoided due to concerns over the aromatic oils they release. These oils have been shown to elevate the levels of some liver enzymes, which can affect the metabolism of drugs and other compounds. If wood shavings are used at all, better alternatives include hardwood shavings such as aspen. Straw or hay is a good bedding material for rabbits. For choices for the litter box, see the section on litter training.
While living alone in an outdoor hutch is a lonely existence for a rabbit, a house rabbit that is allowed time outdoors will likely enjoy the change of scenery and fresh air. There are several dangers in the outdoors, including predators, weather, and toxicity from herbicides, pesticides, or poisonous plants.
Since predators present the largest danger at night, keeping a rabbit outdoors in a hutch at night is risky, even in a city (where predators may include raccoons, cats, dogs, coyotes, hawks and more). Many of these can injure or kill a rabbit without even getting into the cage. If a rabbit is to stay outside, it should at least be in an enclosed shed, garage, or some shelter that allows complete protection.
Many owners allow their rabbits outside in an enclosed pen made form a wood frame with wire on all sides (including top and bottom). This allows bunnies to spend time outside and munch on the grass (provided it is not treated with any herbicides, pesticides or other chemicals!) without burrowing out, and with protection from unwanted visitors. Shelter from sun, wind, rain, and other elements must also be provided.