I would be very interested in any information on Willem II of Orange, but especially would like to know if he had illegitimate children.

I haven't been able to find any, but that doesn't mean he didn't!

In Stephen Baxter's "William III and the Defense of European Liberty, 1650-1702" (a very anti-Willem book, by the way) he says that Willem might have been the father of a certain Abel Tassin d'Alonne, whose mother was Jeanne de Bommert, Willem's mistress. I read somewhere else (unfortunately I can't remember where) that William III was often teased on his resemblance to another gentleman (I can't recall the name) who was thought to be an illegitimate son of Willem's. The "Europaische Stammtafeln" series of genealogical charts often includes illegitimate branches of royal houses, but does not do so for the House of Orange, though there were several Nassau lines descended from Maurits and Frederik Hendrik. I would like to think that Willem might have descendants living today.