Came in expecting this to be "Incredible Crsis: The Thread" and am happy to see it get multiple mentions. Did not expect to see PepsiMan mentioned. Horrible game but I have more time into it than I should probably admit - there's just something addictive about it.
Limiting myself to stuff that I haven't seen mentioned yet:
Eretzvaju/EvilZone - an often forgotten fighter that had some really fun gameplay and interesting characters. Played a whole lot of it with one of my high school buddies.
iS: Internal Section - A very slick shooter published by Squaresoft that feels like a bit of a combination between Tempest and Rez. One of the few games that ran in the playstation's hi-res mode (I think Tobal 1/2 did too).
Elemental Gearbolt - A lightgun game with a fantasy theme, beautiful music, and some gorgeous anime styling. Has GunCon support.
ChoroQ Marine: Q-boat - Everyone knows the ChoroQ line of toys and acing games these days. This is pretty much the same thing but with boats! The gameplay was really good though, and in some ways it felt a lot better to play than the car-based games. May be rose colored glasses on the this one, but I remember it fondly.