Nefarious Plans, 1920’s Glam, and Teenage Flimflam
Dangerous High School Girls is a highly unusual game; set in a rather forbidding girl's high school in the 1920s, you lead a team of girls investigating a series of accidents, and surviving the often-nasty hazing you get from other girls. It is, thus, a story-driven game, but the actual gameplay is almost boardgame like; indeed, the graphics are purposefully designed to look like a vintage game board, and overcoming opponents doesn't rely on combat, but instead on a series of minigames that represent, in some sense, fibbing, taunting, exposing secrets, and making power plays.
Space Trading Goes Gonzo
Take an Elite-style game like Flatspace II. Set it in a cartoony universe where Zombies and Ninjas are waging an interstellar war. Tool around in a "starship" that's more like a Buick with a stardrive and lasers. Wage space battles against, among other things, space-going galleons and pterodactyls, and trade goods like cheese, paper, and kittens--no "industrial goods" or other boring stuff here. All to a loud, frenetic neopunk score--that's Ninjastarmageddon!.
As far as the gameplay goes, Ninjastarmageddon is familiar: You control a single ship, and tool around the galaxy, trading goods, fighting battles, going after pirates as a bounty-hunter, going pirate yourself, and finding and looting derelict ships.

Porno for Pyros
In real life, burning things down is highly antisocial, but then, so are a lot of the things that are fun to do in games.
Play with Fire has novel and interesting gameplay; you win by burning stuff down. If most 3D games have the verbs "move, jump, and shoot", Play with Fire has the verbs "move, jump, and set on fire." The result is something you've never quite seen before.