You can sing any Emily Dickenson poem to the tune of Yellow Rose of Texas. Makes her stuff a lot more entertaining.
Other than that, I recall someone mixed “The Real Slim Shady” with the music for “Oops I Did It Again”, and another mix was the first Slim Shady song mixed with “Funk Soul Brother”
Does Run D.M.C’s version of “Walk This Way” count?
GoHomeProductions makes the best mashups. My favorite is Christina Aguilara’s “What a Girl Wants” mixed with the Velvet Underground’s “Rock and Roll.”
The Kleptones are masters of the genre. My favourite, A Night at the Hip-Hopera, mixes Queen and a large variety of hip-hop artists with awesome results.
If you like mash-ups, you’d probably like the albums of The Avalanches, Girl Talk and The Go! Team. The first two use exclusively pre-recorded material in creating tracks, while The Go! Team mixes samples with live instrumentation to create new songs.
Great thread idea 
The one Cluricaun mentioned is a good one. Others I like are “Closer to Wannabe” Nine Inch Nails vs Spice Girls, “Walking With A Ghost In Paris” Tegan & Sara Vs. Mylo, "Pull Up the Poor Bitches” M.I.A. vs. Mindless Self Indulgence, and “Oops,The Genie Is In The Bottle” Britney vs Christina.
The Beatles’ album Love, for Cirque du Soliel, features mash-ups of various Beatles songs.
“Queen Machine”* by Streetlife is “Bohemian Rhapsody” + Goldfrapp’s “Strict Machine”
*Youtube link
I love mash-ups here. One of my favorite current ones is Rapture Riders, a mash up of Blondie’s “Rapture” and The Doors’ “Riders Of The Storm” done by Gorillaz.
Not really a “goofy pop” tune, but I’ve always liked the song that resulted from a crazed Bungie fan’s melding of the themes from Halo and Myth II: Soulblighter.