Two and a half years after this, here's another mashup made for fun: "Single Ladies" vs "I want candy." [more inside]
Mashup I made for fun, had laying around on my hard drive, and remembered while reading this thread. The tracks are "Crash" from Gwen Stefani's "Love. Angel. Music. Baby." (written by her and Tony Kanal) and "Mr. Xcitement" from They Might Be Giant's "Mink Car" (and featuring Mike Doughty on vocals.) What I like about it is that neither track is an acapella track, and that both singers (like both music tracks) are overlapping throughout, but it still works -- other than a tempo (but *not* pitch) change to speed up "Crash" and a few measure movements/cuts, no other changes were necessary. Note that release of the TMBG/Doughty track predates the Stefani track, and that I cut off the spoken word intro and painfully long musical ending of the TMBG track (which the Stefani track did not overlap) to save you all download time.