Chess.com won't allow an illegal move. Playing OTB I don't know.
Should I claim a win for a illegal chess move by my opponent?

According to rules of chess if a player leaves their king in check or commits any other illegal move their opponent can claim a win but is it fair play?
Under FIDE rules, I believe this only applies in rapidplay and blitz games, not in standard time control games. I guess it's up to you whether you want to claim the win, but you can't say that claiming a win is unfair, since it's in accordance with the rules. (Note that if the arbiter sees the illegal move in a rapid or blitz game, he is supposed to automatically call the win.)
You can read the FIDE rules here (Appendices A and B):
http://www.fide.com/fide/handbook.html?id=171&view=article
According to rules of chess if a player leaves their king in check or commits any other illegal move their opponent can claim a win but is it fair play?