Does 35mm canon rebel lenses fit on canon digital?

All of canon's EF-mount lenses will fit on all camera bodies in the Canon EOS system. Simply, if the lens says "EF" on it, then it will fit any Canon camera that says "EOS" on it.
If it says EF-S on it, it won't fit on a EOS film body or a full-frame digital. EF-S lenses only work on EOS digital SLRs with APS-C sized sensors (Digital Rebel and 10/20/30/40/50D series)
If it says FD on it, it won't fit on any EOS body. These are the old manual-focus lenses from the 70's and early 80's.