Over at The Week, there's an article utilizing the best in theoretical physics (fun!) to determine the longest home run theoretically possible under the constraints of time, space, and human ability.
Turns out it would 748 feet, but would have to be hit by a someone who's 6'8" and ~240 pounds with less than 10% body fat hitting a 111 mph fastball. Sounds simple enough.
But even beyond the fun of physics calculations, the article's got some general fun info about hitting. It's often been said the hardest thing to do in sports is hitting a round ball with a round bat, but when you consider the physics of it, it becomes even more impressive.
Some fun facts from the article include that the average pencil is about twice as big as the margin of error for hitting the sweet spot on the bat and that a 99 mph fastball gets to home plate literally faster than the blink of an eye (395 milliseconds to 400 for the blink).
Go read it, it's worth your 5 minutes...