Not counting anime I used to watch Captain N, Zelda, the various Mario and Sonic cartoons, Street Fighter, Double Dragon and Mortal Combat. Except for maybe the Sonic cartoons those don't really hold up very well today though.
Some of my favorite video game cartoons:
Wing Commander Academy (
http://www.youtube.com/watch?v=_bzEMITUq_w) was really good and as far as video game cartoons go it was one of the most faithful to the source material.
They even got voice actors from the games like Mark Hamill, Tom Wilson and Malcolm McDowell. I've been meaning to pick up the DVDs they released of it just recently.
Also even though it's not based on just a video game, the Battletech (
http://www.youtube.com/watch?v=A-_-8D8R4CU) cartoon was really badass and had an amazing ending.
Mega Man (
http://www.youtube.com/watch?v=akJygsSXcjw) had a pretty absurd cartoon but I always liked it. The theme and its video introduction are still pretty killer.