For me, it was the game Rocket Jockey released by Sega Soft in '96. It was perfect. The game featured a surf rock soundtrack by Dick Dale. The entire premise of the game was to ride around on rockets and using long cables to yank your opponents off theirs. Referees were also fair play. I don’t think I’ve met anyone else who has played the game, so if you have, let me know!
Arcanum
I was totally sucked into the world when I first played it as a kid. The balance and trade offs between tech and magic are awesome and the incredible dialogue and (OK from what I remember) story makes this one I come back to every once in a while.
I don’t think I ever actually have beaten the game though – but I do that with nearly every game.