Another well known attempt (at least in New Zealand) was by Richard Pearse in 1902/1903.
He had some success, but never achieved controlled flight for as long as the Wright brothers, nor did he organise media coverage to the same degree that the Wright brothers.
A well-known attempt was by is Samuel P. Langley, who had had success with gliders and powered models. Was fond of 'tandem wing' designs (one wing behind another). His first serious manned attempt was in 1903, shortly before the Wright bros. He launched off of a houseboat/barge in the Patomac River. It dove straight into the river.
Reconstructed and currently in the Smithsonian:
http://airandspace.si.edu/collections/artifact.cfm?id=A19180001000