Most games are programmed to run in only one specific resolution (the exception being a handful of Doom clones, but playing them at high resolutions is a painfully-jerky experience unless you have a very fast system).
There's a few games out there that differ: I recall RoboSport had the option of playing at 320x200 or 640x400, if you played it in the high res mode you could see 4x as much of the playing field at once. Also supported network play and a few other advanced features, but games which were that "forward thinking" are few & far between!
