Mortal Kombat, Street Fighter II: The Animated Movie, Postal, Detective Pikachu, Sonic 1&2. Not necessary the greatest of cinema, but all of them did a good job of turning the source material into a movie. Probably helps that the source material of all of them is relative simple and leaves plenty of room for interpretation.

Also Steins;Gate, though that's a visual novel turned anime, not a regular game. But probably the best example of staying very close to the source material and succeeding.

I've only seen Mortal Kombat out of these and I guess I have to agree with this one. It was just as cheesy as the game and it worked well.

Elf Bowling loljk Maybe you can count the original animated Pokémon movies as based on a video game.

Silent Hill was pretty decent IMO