Oh man, I like this topic. I'm going to follow Kinzo's lead and avoid recommending Touhou doujins, or games you may have heard of. So let's see:
AirRade Air: Beautiful horizontal scrolling shooter.
Assault Cube: free FPS that can be played offline or online, on any operating system. Loads of dumb fun.
Braid: You must, must, must play this game. Completely redefines what platformers are all about.
Crescent Pale Mist: Odd little game that mixes fighting, platforming, and danmaku.
eXceed3rd Jade Penetrate Black Package: Awesome shmup with great music, great voice acting, and bosses who laugh at you as you fight them. Heavy emphasis on streaming.
Engage To Jabberwock: Combines puzzle gaming, dungeon crawling, and danmaku.
Penumbra Black Plague: Scary as shit horror survival game that really tests your powers of logic.
Trouble Witches: Gloriously animated horizontal-scrolling shooter.