I've seen websites devote so much time to this question. As far as I'm aware the most in depth investigation, taking into account every piece of relevent information possible from every episode (for example, we know that they have the death penalty in Springfield, which immediately rules out a number of States) came to the conclusion that it was impossible for any one State to fit the bill perfectly, but the one which came closest was California. However, I seem to remember seeing something on The Simpsons (can't remember exactly what it was) that suggested Springfield's State didn't have a coastline. Obviously, it is deliberately vague so as to imply that The Simpsons could be taking place almost anywhere in the US. That's the whole point, they are a very average family (not that my dad's ever been into space, won a grammy or mud wrestled George Bush Sr.).
One interesting point, I once saw a reference in an encyclopedic book of terminology and events from The X-Files (also produced for the FOX network in the States) that Homer Simpson was a "yellow skinned resident of Springfield, Illinois", but I belive this just to be the result of bad research on the author's part.