I love “All Through the Night” by Cindy Lauper, but I think the rest of Cindy Lauper’s music is pure crap. One other example I can think of is “A Change Will Do You Good” by Sheryl Crow. What is the single song you like by an artist you otherwise despise?
“Anytime You Need a Friend” by Mariah Carey. I’m not even sure why I like it. But I won’t listen to any of her other stuff.
“Copacabana” by Barry Manilow. It has a real goofy charm, unlike his other songs (I think someone else wrote it).
“Sexy Back” by Justin Timberlake (although I don’t hate the guy, I hate pop music and I don’t particularly like the rest of his music). “True Colors” by Cindy Lauper. That’s about it for now.
“Nights On Broadway” - BeeGees
Inane chipmunks on speed and disco-trash they may be, but this song grabs me.
“Dancing in the Dark” by Bruce Springsteen
“Viva la Vida” by Coldplay
I’ll second the second one. I love this song but hate the band. There’s humour and liveliness to it that seems to me to be lacking in most of the rest of their work.
“Picture” by Kid Rock. I love the song, and intensly dislike him. Ms Crow isn’t on my radar, so I prefer to pretend it’s her influence that made it listenable. Someday, I will hear one of her songs, and may have to abandon that theory.
“Follow Me” by Uncle Cracker. Great song, but it has an obnoxious premise (the concept of no harm-no foul, secret extramarital fucks piss me off), “Uncle Cracker” is a horribly obnoxious pseudonym, plus Mr. “Cracker” utterly destroyed “Drift Away” for me with his nasty name and his smarmy whispery voice.
I love “I’m with You” and hate Avril Lavigne.
“Paint It Black” by the Rolling Stones. I find them otherwise unbearably annoying.
I love Barry Manilow’s version of “Memory”, believe it or not, and cannot listen to anything else he sings. I’m sure I can come up with some other answers to the OP (it’s a good question) but not when I’m sleepy. Instead I misread the thread at first and was going to tell you the song I hate by the group I love (that would be “Miss You” by the Stones).
- … looks around to check that no-one who knows him is within earshot … *
I really like Donna Summer’s version of State of Independence - more than the original by Jon and Vangelis
There, it’s out.
“Bawitdaba” by Kid Rock. I don’t like him at all either, and don’t really like the sentiments expressed by the song, but it’s such a good “crank up the volume” selection.
I’ve seen the “Viva la Vida” recommendations before, and I really am not a fan of that song. I like a number of Coldplay songs enough to… well, pretty much just long enough to enjoy them while they’re playing and then completely forget about the band. However, this song just doesn’t grab me.
Oh yeah, Justin Timberlake’s “SexyBack” is another. I kind of like that song he did with Madonna, “4 Minutes”, but for some reason his name-checking (when he says “Ma-donna”) of her ruins it for me.
The Wheels Contact the Road or something like that by Phish.
I like Pearl Jam’s music, but I change the channel when Eddie’s croaking starts, but damn I like their version of Last Kiss.
La Isla Bonita - Madonna
On a closer examination of the lyrics, you’re right. I always thought it was about a Heroin addict.
For me, it’s “In the End”, by Linkin Park.
It’s because I can relate to the lyrics, which means I should probably kill myself. 
“Welcome to the Black Parade” by My Chemical Romance.
They have a completely horrid and screechy sound most of the time, but in this song it kind of works.
“She Hates Me” by Puddle of Mudd. Mock me if you must (if anyone else even remembers them).
“Rhinoceros” by Smashing Pumpkins.
“Lua” by Bright Eyes.