OTB Question

If your opponent exposes his king to check - can you take his king ? Or does he get to make another move ?

It is against the rules to move in such a way to leave your own king in check.

In tournament chess, if an illegal move is made, once it's noticed the position is reset to the most recent legal position and play continues from there.

In club play usually one player politely reminds the other they're in check when they try to make that illegal move (I usually just touch the checking piece and they immediately take it back).

There are two places I've seen the king capture to win used though.  First is in some blitz tournaments, and second is in informal tournaments with young kids.

If the initial piece that is touched can make a legal move, it must be moved, as well. 

Yes, that's true.  There also may be a time penalty involved.  In my 3rd tournament this happened to me in a time scramble.  I left my king in check, and with 1 second left on my opponent's clock his cat-like reflexes managed to stop the clock and make a claim before it hit zero.  He got +2 or 3 minutes and I ended up losing :(

I once 'captured' the opposing King...when I was twelve! I thought I had done something really great.

thank you.