A mash up occurs when a DJ takes one song and puts its vocal track to the instrumental track of another song. The most famous (or infamous) mash up is probably The Gray Album, in which DJ Dangermouse took music from The Beatle's White Album and mashed it with music from Jay Z's Black Album.
Probably the best masher I've heard is DJ BC. He ripped off the Beatles too by mashing them up with The Beastie Boys--thus creating "The Beastles".
He's done a lot of other tracks too. Technically, you shouldn't be able to download any of this stuff because it's all breaking copyright laws... but you have to hear it. Check out his site and download his stuff here. He's thought of such imaginative collaborations as George Michael vs. Talib Kweli; Led Zepellin vs. The Vandellas vs. Mos Def; Radiohead vs. The Roots; Snoop Dogg vs. The Flaming Lips vs. Will Ferrell (yes THAT Will Ferrell); and The Beastie Boys vs. Kool & The Gang vs. Cyndi Lauper.
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Anyway, do yourself a favor and check this stuff out while you can.