I'd recommend starting with some highly rated (by lots of people) albums... see what ya like :)

Pixies (Doolittle or Best of) - classic guitar indie
Pavement (Slanted & Enchanted) - classic guitar indie
Interpol (Turn on the Bright Lights) - dark guitar indie
Radiohead (Ok Computer) - guitar indie
Grandaddy - (Sumday) - indie space pop
The Postal Service (Give Up) - indielectronica

(ok - grandaddy I slipped into here... but they are great! My fav. band the last few months...)

Dont forget The Flamming Lips "Yoshimi battles pink robots"
Does anyone else think granddaddy sound like the flaming lips?

Sonic Youth "Daydream Nation"
The Velvet Underground" The Best of".
My Bloody Valentine "Loveless"

The Unicorns - Sea Ghost
awesome song :)

Any songs from Hot Hot Heat, Interpol, Bloc Party, Say Hi to Your Mom, The New Pornographers,The Arcade Fire, are all common, good bands to get you into indie

Yeah, VU are pretty much where you want to start if you want to get into indie, they've been an influence on virtually every major indie band.

cheers fellas...

all the help is great. ill start on those bands.

grandaddy!

Radiohead are on a major label. How are they indie?

The New Year :]

There are many 'indie' bands on major labels...

You can't be an indie band and be on a major label.