Physical Danger
Though an infielder or pitcher will take the occasional batted ball right to the head, on the whole baseball isn't dodge ball. No one's deliberately pelting ninety miles per hour balls at players—unless you're the pitcher throwing to the catcher, in which case you're on the same team and the catcher's pretty well protected.
The slight majority of injuries in baseball are non-contact. For the most part, players end up on the disabled list from upper leg strains, ankle sprains, and shoulder strains to name a few. Repetition can also be a long-term danger, especially on catchers' knees and pitchers' shoulders and arms.
That said, every so often a baseball player will end up on the disabled list for something far more bizarre—like a sprained thumb after an overzealous high-five from a teammate, or from punching a wall after a terrible inning. Important rule: in a fight against a wall, you will always lose.