Self-eliminator sounds fun. I teach an AI class, and one of the assignments is always to implement a board game with adversarial search. In some semesters I have assigned games that included the self-eliminator feature, and it invariably leads to some clever moves, while not changing the fundamental nature of the game all that much.

A few other variants that I like are:

Krigspiel - takes separate boards and a mediator. Players are given hints as they are moving, and they need to deduce where the opponents pieces are. This is a famous and old variant. I've only played it 2 or 3 times in my life, as it isn't as convenient as other variants.

Progressive - In this game, the first player gets one move, then the opponent gets 2 moves, then the first player gets 3 moves, etc. In 1996 I played in the first World Progressive chess championship - organized over the internet, and it drew some 60 players ranging from masters to duffers. The results and all the games are still up on web. I made it through to the final round, and ended up in something like 8th place. It was the most nerve-wracking experience I've ever had in chess, and I'll never play that game again unless it's blitz with a clock. Interesting trivia, the winner of the tournament, Fred Galvin, is credited as the inventor of refusal chess!

Smess - Not really a chess variant, but a chess-like board game in which the pieces move according to arrows drawn on the squares. A fun and easy game to play.