[link|http://www.elections.state.il.us/elecinfo/pages/downloads/pdf/R-19.pdf|Here] is the Illinois Voter Registration Application R-19. Nowhere on there does it ask for your party affiliation.

I've been registered to vote in 3 states during my lifetime (New Jersey, Texas, and Illinois.) The only times I ever had to say which party I was voting for was during primaries, where you're only allowed to vote for one set of candidates. That does not necessarily declare your party affiliation, however, because you could be a life-long fully-registered Republican, but if you want to vote in the Democratic primary to attempt to get "the easier guy for your guy to beat" to win the Democratic primary, I've never heard of any laws disallowing that.