This link came from the July 16, 2013 installation of Marriage Moats by Lori Odhner. It's a Japanese phone commercial, and that phone SHOULD be bought, because they really earned it with this project!
There is a game for Android, iPad (and other touch-screen games, I guess) called Magic Piano. As you touch the dots, coming down on the screen, the notes are played. It can be for points, or competitive, or not, depending on the options you choose. The game will play it for you so you can hear the way it should be. It won't need to be that fast, though. Some are very simple and some very complex. It's free to play, but you can add on other things for points or cash.
On some of the songs, it works better to use two hands, and some (a couple of the Bach pieces) I know from playing piano and can get through by remembering the fingering patterns.
Holly has a tiny violin played note-by-note by drawing its bow across, and the rhythm of the bow strokes plays the song. I'll try to get a video of that.
Are there other such toys or games?
At a gathering of collectors of mechanical musical instruments at Hollycombe Steam in the Country in July 2013:
That's me singing... but I started singing a parody version. It's "The Sweet By and By."
The photo above is of a hurdy-gurdy. Since this one's in The Netherlands, it's a draailier [their term for it: from draaien (“to turn”) + lier (“lyre”)]. Here is a video of another such instrument at the same museum another time. My photo above; someone else's video below.
Other instruments have a mechanical aspect: Autoharp, piano, harpsichord, pipe organ, reed organ.
From the Australian Broadcasting Company:
"Mechanical musical instruments