**Undetermined.**

The mystery is an **intentional [running gag][1]** and their true state of residence is never revealed. Instances when it *does* seem to be revealed or at least approximated are usually illogical, altered later or contradicted with some other information. From [Wikipedia][2]:

>Because of the many contradictory statements regarding Springfield, it is impossible for the town to exist in a specific state.

And [Wikia][3] elaborates:

>The uncertain location of Springfield is a running gag in the series, based on the fact that 34 states in the United States have at least one community with that name; and several have more than one. Episodes frequently make fun of the fact that Springfield's state has never been revealed, by adding further conflicting descriptions, obscuring onscreen map representations, and interrupting conversational references. 

For example in *The Simpsons Movie*, Ned Flanders says that the state borders Ohio, Nevada, Maine, and Kentucky, which is an impossibility. And in the episode [Behind the Laughter][4] they're revealed to be from North Kentucky, but this was changed to South Missouri in reruns (and the show is revealed to be fake there anyway, so it could just be the *filming location*). 

You can find many clues as to where Springfield is or isn't in the above, quite thorough Wikia page (including the fictional state North Tacoma), but in all likelihood these were deliberately planted there. It's unlikely that they'll ever let this gag go and that we'll ever get a definitive answer (certainly not now, with so much conflicting data). It's best to just enjoy the ride and [not play into their hands][5]. :)


  [1]: http://tvtropes.org/pmwiki/pmwiki.php/Main/WhereTheHellIsSpringfield
  [2]: https://en.wikipedia.org/wiki/Springfield_%28The_Simpsons%29
  [3]: http://simpsons.wikia.com/wiki/Springfield's_State
  [4]: https://en.wikipedia.org/wiki/Behind_the_Laughter
  [5]: https://movies.stackexchange.com/questions/24650/is-fezs-country-ever-revealed