Will American PlayStation 3 games work on a European PlayStation 3?

yes the ps3 is a universal system which means you can buy PS 3games from anywhere on this planet and they will play on any system, this was a new installment sony made when creating the ps3, because in the past the ps1 and ps2 are not universal

BEWARE!!! PS3 IS A REGION FREE CONSOLE BUT SOME GAME MANUFACTURERS MAY REGION LOCK THE DISCS. I'D LOOK IN TO IT FIRST BEFORE YOU MAKE ANY BIG BUYS.