Like the origin of Easter, the origin of the Easter Bunny has roots that go back to pre-Christian, Anglo-Saxon history. The holiday was originally a pagan celebration that worshipped the goddess Eastre. She was the goddess of fertility and springtime and her earthly symbol was the rabbit.
Thus the pre-Christian Anglo-Saxons worshipped the rabbit believing it to be Eastre's earthly incarnation.
When the Anglo-Saxons were converted to Christianity, the pagan holiday, which occurred around the same time as the Christian memorial of Jesus' resurrection from the dead, was combined with the Christian celebration and given the name Easter.
Originally, there were some very pagan practices that went along with the Easter celebration. Today, Easter is often commercialized, with all the focus on eggs, the Easter bunny, etc.