Sudden Death Chess is a variant I entered in chessvariants.com's 32-Turn Challenge (a contest to produce a variant guaranteed to end in 32 or fewer moves) in April 2000.    Incredibly enough, it came in 3rd place.
 
The rules are the same as normal chess except:
1. When a player makes a non-capturing move, he must remove one of his pieces immediately after that move.
2. If a player is forced to remove his own king, he loses.
 
The ZRF also contains Sudden Death Extinction Chess, which is Extinction Chess except:
1. When a player makes a non-capturing move, he must remove one of his pieces immediately after that move.
2. If a player is forced to remove his own king or queen or his last pawn, rook, knight or bishop, he loses.