There are many things that can cause a rabbit to limp:
Rabbits have very fragile bones that can break easily.
Broken bones will cause limping and reluctance to move. Rabbits will often also eat less if they are in pain.
Arthritis is inflammation of the joints and is very common in older rabbits. It can however also affect younger rabbits, especially giant breeds. Arthritis is painful but there are lots of things you and your vet can do to keep your rabbit as happy and pain free as possible.
Wounds and injuries
Wounds, sprains, strains and bruising all cause pain and are likely to make a rabbit limp.
Spinal injuries can paralyse a rabbits back legs, these are particularly common if a rabbit is dropped or jumps from a height.
Bumble foot (also known as pododermatitis) is an infection that causes a painful, swollen, crusty areas on the bottom of the feet. Sometimes it is caused by a wound, but it can also be caused by wire flooring or hard flooring in their enclosure. Bumble foot infections are extremely painful.
If a bone comes out of its socket (such as a hip bone) it will be extremely painful and will often mean the rabbit is totally unable to use that leg.
If your rabbit is overweight, they may move around less as well as having extra stress put on their joints. This can make them stiff and painful. Read more about how to XXX keep your rabbit in shape.
Some tumours can grow large enough to prevent legs moving normally, or they can grow in painful places and cause a limp. Bone tumours are especially painful and cause many of the symptoms above.