Depends on what you mean by normal hay. Timothy is a grass and grass hays are all suitable for rabbits. Timothy just happens to be popular and available in most areas. Other grass hays include brome, orchard grass, Bermuda hay and oat hay. Some people are allergic to timothy, but are fine with other types.
Alfalfa is a legume hay. It is higher in protein and calcium, so not good for adult rabbits, but is fine for younger ones and those who may need some extra nutrients.