What sports have the greatest likelihood of injury for amateurs?

Tough to say. Any activity can be safe or dangerous. Someone who has never skied is more likely to get hurt than an amateur who skis every year, but is this more likely than a person who goes out to play tennis or basketball? The main focus should be on making sure you have the proper conditioning before participating in impact sports. Jumping, bursts of speed put a lot of stress on tendons and ligaments.
Contact Sports. All sports have a likelihood for injury.