Anything basic will do. Try not to stress heaps over the process of learning guitar. In the beginning, individual song choices aren't that important. What music are you into? Try and pick something that you connect with.
"We weren’t too ambitious when we started out. We just wanted to be the biggest thing that ever walked the planet."
-- Steven Tyler
"Radiohead - Creep" is a pretty good song to practice barre chords.
Any Stephen Lynch song, Flight of the Conchords and some Tenacious D stuff, and house of the rising sun.
Counting Crows - Round Here
Radiohead - Karma Police
Howie Day - She Says
Try some of these:

These are decent easy songs (Standard A440 tuning):

Warren Zevon, Exciteable boy E,A,B

Warren Zevon, Poor poor pitiful me C,G,D

Warren Zevon, Werewolves of London, E, D, C, G,

Beatles, Get back A,D,G

CCR, Bad moon Rising D,A,G

CCR, Down on the corner, C, G, F

Jimmy Buffet, Margariettaville A,D,G

Alice Cooper, Escape E,B,A (with C,D,B in the bridge)

Dave Edmunds, Almost saturday night D,G,A

Judas Priest, Livin' after midnight C,D,A,G

Roger Miller, England Swings D,A,G

Scorpions, No one like you A,F,G,C

BTO, You ain't seen nothing yet, A,G,D - A,E,D in chorus.

Gordon Lightfoot, Sundown, F#, B,E,C#

Paul Simon, Me & Julio down by the school yard, A,D,E

ELO, DoYa, D,A,G

Foghat, Third time lucky, C, F, G

Sweet, Little Willy, E, A, B (go one step up at the end, F#, B, C#)

Sweet, Fox on the run, B, A, E

The Who, Can't explain, E, D, A, B

Albert Hammond, It never rains in So. Calif. , B, E, A, F#

Johnathan Edwards, Sunshine, Bb, F, Eb, G#

B.W. Stevenson, My Maria, E, B, A

Bad Company, Can't get enough, C, Bb, F, Eb

Dokken, Breaking the chains, E, D,C, G

Twisted Sister, Bab boys of R&R, D, G, A, C#

Twisted Sister, We're not goinna take it, Song start E, Eb,C#, B (barred hi chords)

E, B, A for the rest.

Twisted Sister, I'll never grow up, B, E, F#

Niel Young, Rockin' in the free world, E, D, C (chorus G, D, C)


Those are the most used chords in those songs.Based on what *I* hear.

I am not a pro so corrections welcomed!

Updated 11/18/07
"My best advice to anyone who wants to raise a happy, mentally healthy child is: Keep him or her as far away from a church as you can." - Frank Zappa
Hmm, I never really learned any songs that had chords in them that helped me with guitars. I just made up chord progressions that sounded good to me and were also on the chords that I needed to work on so I got practice the last one was probably A13, B11, G13, Amin11
Fender Stratocaster MIM
Jackson DX10
Epiphone Les Paul Custom (neck: Seymour Duncan Jazz, Bridge: Seymour Duncan Distortion)
Marshall Mg50dfx
Digitech Metal Master
Crybaby 535Q
Try some Tom Petty... Maybe some CCR... a little bit of Ac/Dc...

Most of the classic rock songs revolved more around chords than around the concept of playing a million notes a second like you find in most of todays music.
If were talking real basics then Seventeen - The Sex Pistols. Simply: A - D - A - E
Quote by Steve The Plank
Try Green Day - Good Riddance(Time of Your Life)? Everyone seems to know that song.

+1 i started to play that at my school and everyone in my music class just started to sing it.