Hard to say... there's been a few games which get pretty much ruined by their adaptions...
So far I know of:
Ape Escape spawned an anime and now even a western cartoon. The anime was average at best(I'm not sure what to think of it... sometimes its funny, but it can also be quite dumb), I haven't seen the cartoon but by the looks of it (two minute shorts on Nickelodeon) I'm not impressed.
Super Mario too has a wstern cartoon, a live action movie and I think there actually is an anime too.I've only seen the cartoon, and its stupid. The LiveAction movie scares me with its existence.
Sonic the hedgehog has at least two western cartoons and an anime (Sonic X) Where I prefer the SaTM-cartoon of all. The other cartoon is just silly, and Sonic X was.. confusing.
Kingdom Hearts has a manga adaption. Its kind of funny..
Final Fantasy has Advent Children (which a lot of people seem to hate... I liked it a bit)Last Order, and some other series I only saw a couple of episodes from before getting bored.
Pokèmon has one anime and SEVERAL manga-adaptions.The anime has lasted too long and overused just about any plot they had (which was always thin if you ask me) If they should try again I'd prefer an anime of Pokèmon Special(which follows the game-story more accurately than the anime does)