I own three keyboards: one for typing, two for playing music on. The one for typing is the only one I know how to use though, so I'm pleased with Touch Pianist. It's a website in which you press any key in order to advance a piece of classical music one note at a time. It's unlike Guitar Hero in that, if you stop typing, the music stops playing, but there's still challenge if you need it in trying to match the rhythm of your key presses to that of the original piece. It's quite lovely.
John linked me to this and I had a brief moment of either snobbery or of simply not getting it. It's close enough to the likes of Guitar Hero and Rock Band to invite the comparison, but with the dexterity and timing that makes those games satisfying removed such that it Touch Pianist seemed nothing-y, or like a crank-powered music box. But then I kept playing and had fun trying to keep rhythm with the music and experimenting with different songs and tempos. In this way, it's more like Audiosurf than the those other rhythm games, and it entertains because it's a more engaged way to spend time with music.
I recommend trying Presto Agitato from Moonlight Sonata.
If you like it a lot, there's an iOS app that does the same thing but which has in-app purchases for other pieces of classical music. They seem to mostly cost $0.99/£0.79 each.