There is a lot of piano literature for one-handed play. There is even a guide, "One Handed: A Guide to Piano Music for One Hand" which surveys over 2,100 individual piano pieces for either playing with the right or left hand alone.
Since most people are predominately right handed, the right hand and arm are injured more often than the left hand so 99% of all piano pieces written for a single hand are for the left hand.
Last month, according to USC's Thornton School of Music, Kinsey won Grand Price at the 2014 Debut Concerto Competition playing Ravel's Piano Concerto for the Left Hand in D major.
One-handed piano music is not only for people with injuries. Actually, learning to play music written for a single hand can be fun and serve as a break from the usual routine and it can increase the technical ability of the hand which can help when playing music with two hands.