You may be arrested for vagrancy if you do not have at least one dollar bill on your person in Illinois.
If you're not aware of politics in Illinois, it's mostly shenanigans with occasional legislation(just look at our past three or so governors, including Blagojevich, in case you needed something to google), so I'd imagine this is so the good people can be asked for bribes at any time.
In Champaign, Illinois, it's illegal to urinate in a person's mouth.
Was that such a problem that they needed law enforcement to get involved? Although it is essentially a university town. I really have no idea if it's a party school or not.
In Chicago, and I'm just reading off a website, I'm no law student;
It is forbidden to fish while sitting on a giraffe's neck.
That one may sound weird, but considering how often animals escape from the Chicagoland zoos, that's very understandable.