Maybe this is a stretch, but their are some songs that I really like that fit this category.

For instance:

Innocence Mission - Sweep Down Early (I listened to it over and over last summer)

Fastball - The Way (More of a one hit wonder I suppose)

Ian Van Dahl - Castles in the Sky (My favorite dance song)

Zero 7 - Waiting Line (Garden State sound track)

Lush - Ladykillers
Von Bondies - Cmon Cmon
Three Dog Night - Momma Told Me Not to Come
Canned Heat - Going up the Country
Dexy's Midnight Runners - Come on Eileen

I really want to get a Lush and Dexy's Midnight Runners album though...

There She Goes by The La's. (Well, I did hear their album years after the fact, but I still like to think they only had one song. Also- don't anybody ever cover this song again, okay?)

Promise Ring - "Why Did We Ever Meet?"
Dinosaur Jr. - "Feel the Pain"

Interesting thread.
I searched my computer finding all the bands to see which fit the category and considering the amount of music on there, this trend did not occur often (even one-hit wonders like Pure and Fastball had 3-5 songs each).
The New Deal - Deep Sun
Von Bondies - C'mon C'mon
Apollo 440 - Can't Stop the Rock
Compound Red - Open Air Arms
The Cult - She Sells Santuary
Faithless - Mass Destruction
English Beat - March of the Swivelheads
Mae - Suspension
Gary Jules - Mad World
Ok Go - Get Over it
The Shining - Quicksilver (I've tryed so hard to find more from this band, all to no avail)
Stabilo - Everybody
Handsome Boy Modelling School - World's Gone Mad
Uncut - Understanding the New Violence
Ween - Transdermal Celebration