Alright here is a variant that I thought might be good for Brainking. I do remember reading about it on the internet somewhere so no idea if it is copyright or not.

It has the same standard chess setup. 8x8 board. Same usual pieces in chess.
It works like regular chess, in other words you have to checkmate the enemy king.
The difference, is that you CANT put the rival king in check. Check is an illegal move. You can only check the rival king if it is a checkmate.
This means that you can move your own king into a position where it is in check by another piece. In that case, your opponent must stop the check, either by blocking the check or moving away.
If you do move your king in check, you should NOT be allowed to move it to a spot where it is attacked by 2 or more pieces. As that way it would be a win if you moved your king to where it was attacked by 2 enemy pieces.

Basically,
Check is illegal
You can move your own king into check (only if the square is attacked by just one piece)
Opponent must stop the check (move or block)
You win when you checkmate the opposing king