**Undetermined.**

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

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

[Wikia][2] 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. 


  [1]: https://en.wikipedia.org/wiki/Springfield_%28The_Simpsons%29
  [2]: http://simpsons.wikia.com/wiki/Springfield's_State