Self-contradictory songs...
 

There are some songs where the music doesn't seem to fit the lyrics. For example, the song Train in Vain, by The Clash is a rather sad song about a guy dealing with a breakup but the music for the song has a happy-go-lucky feel to it that just doesn't feel right when compared to the subject matter.
Another example would be Guerilla Solder, by Gowan. It's a song about the horrors of war but the music is, again, this happy-go-lucky tune that one might sing to cheer themselves up or pass the time away.

Can you think of other songs where the lyrics don't match the music?

I can't think of any off the top of my head put it's I know if I sit down and think about it I could come up witha few. It's just another way to make the song stick out.

Free Four by Pink Floyd (from "Obscured by Clouds")

"You're Gorgeous" by Babybird?

Outkast "Hey Ya"

Frank Wilson "Last Kiss"

The original song didn't have the melencholy feel of the Pearl Jam version. It was way too upbeat.

They Might Be Giants - They'll Need A Crane....the music is as quirky and up beat as can be expected from TMBG...but the song is about a man whose life is ruined by alcoholism

Yes, yes, and yes.

'"hardcore" - by the german band knorkator
it is a song about hardcore metal, but the song itself is a ballad

any song by Mr. Bungle

Isn't it Ironic?

:p

The theme from Ghostbuster. I mean, ghosts are scary, and that song is all like, get up and dance.

Hahahaha that made my day.

I feel bad for not being able to provide artist, title, OR album, but I have a song...
It's from an album called either "Wackiest Songs" or "Craziest Songs" or something, it's some CD in my girlfriend's collection that she put on when we were on a long car trip a couple days ago. It's this nice little ballad with a pretty happy beat, but it's all about this brave, who is on one side of this big river, and his maid, who is on the other side. They're in love, but can't get to one another because the river sucks so much. One day they decide they can't take it anymore and they both jump in the river. They swim towards each other and meet in the middle, where their hands and lips touch, then get pulled under by the river and are together forever in "the happy hunting ground."

The one with running bear and little white dove?

I'd go for '1970' by The Stooges. Iggy keeps telling us "I feel alright", but the music is all angry and not-alright.

The tune from "Prison Sex" by Tool does not fit the lyrics at all. If you don't listen to the words you could be forgiven for mistaking it as a happy song.

"Things She Said" from Toy Matinee. Very happy, upbeat go get 'em music, and some of the most depressing, rip your heart out and feed it to you before it stops beating lyrics you have ever heard.

"Mozambique" by Bob Dylan. On the outside it seems like it's all about fun in sun, but the song is actually being ironic and commenting on all the killings down there in the 70s.

Like a Rolling Stone- Dylan

Yeah, I'm not sure if it was meant to be ironic that most (if not all) of the stuff she mentions is not ironic. Unfortunate circumstances doesn't mean that it's ironic!

Trapt - Still Frame

The song is talking about how he is someplace he doesn't want to be, and upset about it, yet the music is very uplifting.

Rock and Roll Is Dead - Lenny Kravitz

Sounds pretty rock 'n' roll-y to me

Absolutely! Most of TMBG is like that. "'Til my Head Falls Off" is way upbeat, but it's about a guy who feels like crap. "Twisting" is sounds like a 50's love song, but the Lyrics begin "She set your goldfish free, and now she's sighing. Blew out your pilot light, and made a wish," and get more violent from there. "Don't Let's Start" and "Everything Right is Wrong Again", song 1 and 2 on the very first album. Even their one Love song, "She Is an Angel" has this poderous Thump Thump Thump beat, and is mixed with menacing lyrics. Absolutely brilliant. One of the John's said something to the effect of "There is a thrread running through our music that is relentlessly dour."

Some more - the last two movements of Jethro Tull, A Passion Play, are about Lucifer and flight from lucifer, and they sound like a bloody calliope.

It always strikes me as odd when a classical poem is set to heavy metal - Iron Maiden's "Rime of the Ancient Mariner" or Rush's - "Xanadu"

Of course, this is part of Weird Al's stock in trade. "One More Minute" sounds like a love song, but is really about the agony he would undergo to avoid ever again spending time with the girl. Making his parody of McArthur Park about "Jurassic Park", or All about the Benjamins into "All About the Pentiums" or Gangsta's Paradies into "Amish Paradise", and of course, playing a snippet of Marylin Manson's "The Dope Show" in one of his Polka medleys.

Two just awesome covers that are complete musical inversions of the original songs, to the point of irony - The Cardigans cover of Black Sabbath's "Iron Man", and the Gourd's Bluegrass cover of Snoop Dogg's "Gin and Juice".

Yes that's absolutely it. I'm not the only one to have heard it, amazing!

Belle & Sebastian - a nice, happy, dancelike tune about sexual harassment in the workplace, or something.

There's a good band for irony.