Some songs work better than others... some are simply combined because they are so different, and may match for a part of the song but sound sour or off-key in others. Similarly, the ones that use a rap vocal are almost too easy... as long as the vocal rhythm meshes with the rhythm of the track you've got a nice finished product without having to worry about the clash of dissonant notes.
Here I present the two most perfect mash-ups I've ever heard. I came across both pretty early in my experience, but they have yet to be beat. In both cases, the songs use a vocal by an R&B chanteuse. Also in both cases, everything meshes PERFECTLY... the tune, the rhythm, the natural peaks and valleys of the track. It's like they were always meant to go together. So even if you don't like the singer, or if you don't like the musician, you should still check these out, as the result of the meld produces a sublime hybrid...
Bootystition by Beyoncé vs. Stevie Wonder
Girl Wants Rock 'n' Roll by Christina Aguilera vs. Velvet Underground
These next two are examples of strange hybrids that just work, like getting your chocolate in my peanut butter. Beyoncé seems to be particularly suited to mashing up, as I could've chosen at least 3 others by her... but Beyoncé and Fugazi?! The Outkast vs. Devo track answers the question of how a blending of self-described descendants of brain-eating apes (Devo) and Atl-liens from outer space (Outkast) would sound. One last note... there's no label info on these because mash-ups are very seldom released through traditional means. Instead, they're created by DJs and posted on the internet... so go surf for some great finds of your own!
Independent Room by Destiny´s Child vs. Fugazi
Whip Ya by Outkast vs. Devo