Throughout the history of Fox's hit show "The Simpsons", the state they live in has been obscured. This running gag can be deciphered quite easily if you follow the clues.
Logic places them in Oregon. Matt Groening grew up in Portland, attending a school that looks very similar to Springfield Elementary. Many characters have names of streets in Portland, i.e. Ned FLANDERS, Mayor QUIMBY, Milhouse VAN HOUTEN, Reverend LOVEJOY, the local bully KEARNY, and Sideshow Bob TERWILLIGER. Evergreen Terrace, the street on which the Simpsons live, is also a street in North Portland. Krusty the Klown is based on a Portland-based clown known as Rusty Nails. Finally, Portland contains a (inoperational) nuclear power plant.
There is also proof within the show. In the episode "Round Springfield", Bart buys a record that costs $500, and he pays exactly $500. What is significant about this? He doesn't pay a sales tax! This narrows it down to either Oregon, or one of the New England states, possibly Vermont. The Springfield local radio station has the call letters KBBL. The initial K means that it is located west of the Mississippi River. Thus, Oregon is the only possibility.
More subtle allusions are there. The episode where Springfield is divided into two area codes aired right after Portland went through a similar scenario, albiet without a wall dividing the town. When Albuquerque tryed to steal the Isotopes from Springfield, the Portland Rockies were forced out of town and replaced with the Albuquerque Dukes.
So, as you can see, the mystery of where the Simpson's reside is no mystery at all...if you follow the clues.
Incidentally, the "Behind the Laughter" episode states they are from Northern Kentucky. I have two theories that can explain this. First, they were originally from Kentucky, but moved to Oregon. Second, that episode treated The Simpsons as a show performed by actors. Thus, the actors are from Kentucky, but the show is set in Oregon.