http://osu.ppy.sh/It's a rhythm game--circles and sliders pop up on the screen; click them and drag them with the beat.
Free, and a very active community making beatmaps for it. The interface is almost Macintosh-like, which in this case is actually a good thing--it's tremendously usable; the game is simple but the interface is pretty darn shiny.
When you first start off, you'll need to get some beatmap packs under Beatmaps -> Beatmap Packs. Unzip them straight into your 'songs' folder inside your Osu! folder. You don't even need to restart the program, it'll find them next time you go to the song list. The packs can be very big, but oh well. Make sure you get Internet Pack 1, because it's awesome, and Beatmap Pack 93 is my other favorite so far.
After playing it for a few days I can take most four-star songs (on a five star scale), and I'm starting to make my own beatmaps. I was very sad to discover that The Pillows (who did the music for FLCL) have very inconsistent BPM, so now I'm doing music from Wolf's Rain and Iji. Again, making beatmaps is pretty darn easy from a technical standpoint (of course it's a creative challenge), and submitting drafts is built right into the game...drag an MP3 into the editor, make your beatmap, press 'upload', bring up the IRC tab and type /np to give people a link to your song, get feedback.
It really doesn't take long for this game to give you visual kinesthesia from every song you hear.