XKCD considers what would happen if a baseball were thrown nearly at the speed of light:
After about 70 nanoseconds the ball arrives at home plate. The batter hasn't even seen the pitcher let go of the ball, since the light carrying that information arrives at about the same time the ball does. Collisions with the air have eaten the ball away almost completely, and it is now a bullet-shaped cloud of expanding plasma (mainly carbon, oxygen, hydrogen, and nitrogen) ramming into the air and triggering more fusion as it goes. The shell of x-rays hits the batter first, and a handful of nanoseconds later the debris cloud hits.
When it reaches the batter, the center of the cloud is still moving at an appreciable fraction of the speed of light. It hits the bat first, but then the batter, plate, and catcher are all scooped up and carried backward through the backstop as they disintegrate. The shell of x-rays and superheated plasma expands outward and upward, swallowing the backstop, both teams, the stands, and the surrounding neighborhood—all in the first microsecond.
The article concludes:
A careful reading of official Major League Baseball Rule 6.08(b) suggests that in this situation, the batter would be considered "hit by pitch", and would be eligible to advance to first base.
The Dish 