It is sort of an odd thought really when you consider there aren't very many games being produced without cinematics in the game already. Video game themed movies have really suffered in the past, and I'm sure each director thinks they will be the one that will change how that is, and each one has suffered the same fate. You simply can't make a movie about a video game that will please everyone (as I'm sure the WoW stinkbomb will prove).
Mass Effect seems ripe for the idea, but really the game kinda already plays like a movie, so I agree with KylethePeon's response there. GTA might not make a HORRIBLE movie, as long as you used a character from GTA:VC, GTA:SA, or GTA 4. You really need a character who can talk! VC would almost seem like a ripoff of Scarface, SA would seem sorta like any urban movie from the 90s, so I suppose that leaves GTA 4 open.
If you could base the idea around Niko cutting out an empire in Liberty City and shooting a lot of people for about two hours (at least, horrible that game movies last about 90 minutes) without anyone calling to "go see huge fake American titties cousin!", we'd be pretty good unless they stuck that in as a comedy relief moment during a heated firefight. If it was cast like District 9 with no-name actors to keep preconceptions out of the way, you might have a chance. And keep away from the Micheal Bay practice of explosion after explosion. Maybe one scene with an RPG, but keep it to pistols, SMGs, and ARs. Keep it gritty, urban, and the hell out of New York already. Quite sick of every stinking year some movie is based in New York. Admit it, it may have potential.