I've coincidentally heard a couple of songs in my iTunes rotation lately that have used typewriters as percussion, which made me wonder what other such songs there were.
Internets to the rescue! It turns out that there's a TV Tropes page about this: Rhythm Typewriter. (Reminder: Major time sink. Following TV Tropes links is hazardous to one's ability to get anything done.)
There's also an ilxor.com thread on this topic; link is to the Google cache of the page, 'cause I can't load the regular version of the page.
The two typewriter-percussion songs that I had encountered recently are “Embassy Lament” from Chess (the typewriter bits are in the middle and at the end; presumably weren't done with an actual typewriter, but clearly meant to sound like one), and Dolly Parton's “9 to 5,” the theme song of the movie by the same name. TV Tropes says Parton made the typewriter clicks by tapping her nails together; interesting if true.
The third song that I recently encountered that sounded typewritery is Buddy Holly's “Everyday.” TSOR doesn't turn up any evidence that the percussion in that is actually a typewriter, so I'm guessing it's not, but it sure sounds like one to me.
(Cue y'all youngsters saying, wide-eyed and innocent-looking: “Unca Jed, what's a typewriter?” Kids these days. Get off my lawn!)