The artists/songs in this post are or were indie musicians at the time the commercials came out. Click the title/info to see a link to the videos. I'll edit and add more to this list as I remember/come across them. I'm also excluding things from Apple commercials.

Modest Mouse - Gravity Rides Everything: Nissan Quest Commercial
When this commercial aired, Modest Mouse was about 10 years old, but no one had ever heard of them. The album the song came from sold terribly, in major label terms anyway. It was from Modest Mouse's major label debut after a solid 4 or 5 albums on indie labels.

Jose Gonzalez - Heartbeats : Sony Bravia
Jose Gonzalez is a Swedish born singer/songwriter. He's had almost no success in the USA, although was a bit popular in Europe and Austrialia. This commercial actually hits two indie artists with one stone though, because the song is a cover of another Swedish group, The Knife. The original version is synth laden and just as beautiful. And for a bonus, found this on the tube. Same commercial with The Knife's version. Kinda hard to believe that they're the same song!

Spank Rock - Bump: Wishbone Salad Dressing
Spank Rock is not unheard of. They've had some "hits" such as "Rick Rubin" and the song in this commercial "Bump." But they don't fall into the category of mainstream hip-hop. Since they're on an indie label, they can be on this list.

Nick Drake - Pink Moon: VW Cabriolet
Nick Drake didn't find too much success in the US until after he died. He also got a lil popularity bump from the Garden State movie which had a pretty famous sound track.

Jeff Buckley - Hallelujah
I never saw this on TV so I'm not sure if it ever aired, but it's not the first place I'd expect to find Buckley's amazing cover of Leonard Cohen's Hallelujah. Buckley's version is pretty famous as well as the song itself (Rufus Wainright's version is in Shrek).

The Cool Kids - Black Mags: Rhapsody
The Cool Kids are an indie hip-hop group which are actually on tour opening up for the next artist on the list, MIA. Future versions of the commercial cut out the Cool Kids leaving only that insanely annoying Sarah Ba... too lazy to look up how to spell her last name.

MIA - Galang: Honda Civic SI
MIA is a British woman of Sri Lanken descent who is incredibly different. Just listen to her last two albums and you can see just how truly independent she is from any definition of normal. I tend to think that it's awesome and I was pretty shocked when I heard Galang in a civic commercial. Update! MIA is now featured in a trailer for the movie Pineapple Express. The song is off her latest album and it's called Paper Planes. And in case you're wondering, the gunshot sounds were already in the song!

Of Montreal - Wraith Pinned to the Mist And Other Games: Outback Steakhouse
I had no freaking idea this was an Of Montreal song originally. All I have to say about that is... wow. Here's the original version.

Apples In Stereo - Let's Go: Samsung Instinct
Apples in stereo are an indie band that associates itself with Neutral Milk Hotel and Of Montreal. This one is a twofer tho, they're also in this Dodge commercial.

Mates of State - For The Actor: AT&T Wireless
Mates of State is a cute little indie duo. Husband and Wife kinda like the White Stripes (were). Keyboards and drums though, no guitar.

I also found this blog post with a long list of commercials with information on the artists in the commercials. Some info overlaps with this post.