Even if this shit flops I feel like sharing. I have all the albums these songs are from.

Arcade Fire - Neighborhood #2 (Laika) Well, if you've already heard The Arcade Fire, you've probably heard this song.
Album: Funeral

Aphex Twin - Fingerbib (demo version) - Okay I haven't heard any non-demo version of this song but it's my favorite Aphex Twin song.
Album: Melodies from Mars

At the Drive-In - Rascuache
Album: Vaya

Hot Club de Paris - Snitches Get Stitches Kinda indie/pop rock band from Liverpool. More upbeat/goofy/catchy. I like the chorus.
Album: Drop it 'til it Pops

LCD Soundsystem - Daft Punk is Playing at My House - The ode to daft punk oughta give you an idea of the genre (more of an actual band with instruments though). Catchy.
Album: LCD Soundsystem (Disc 1)

Mewithoutyou - In a Sweater Poorly Knit - I actually like this band for the drumming a lot of the time but this song is more focused on vocals and guitar. However, upon listening to it again while uploading this, I like the drumming too, actually. I really love the lyrics to this song, though.
Album: Brother, Sister

Mewithoutyou - O, Porcupine - Okay talking about mwy's drumming makes me want to upload this song. I love the drums all through the song.
Album: Brother, Sister

Neutral Milk Hotel - King of Carrot Flowers pt. 1 - This is my favorite NMH song, not to mention a contender for my favorite song. I don't particularly like a lot of their songs (that I've heard), yet this remains as easily one of my favorite songs.
Album: In the Aeroplane Over the Sea

Oh No! Oh My! - Walk in the Park - Upbeat catchy indie. The guy's voice is kinda high but you can't hate, it's so catchy. Ba ba ba, ba da ba da ba ba. . .
Album: Self-titled LP

Queens of the Stone Age - Misfit Love - My favorite song off the new CD. If you've ever find yourself enjoying QoTSA but don't have the new album, give this song a listen.
Album: Era Vulgaris

Ratatat - Kennedy - My favorite Ratatat song. Instrumental band with guitar and synth.
Album: Classics

Shellito - 1 2 3 4 - Another band with a keyboard and a catchy riff.
Album: Benevolent Laser

This sounds like a good idea for a topic.

Animal Collective - For Reverend Green - It's off their new album, and is one of the best songs. If you've never heard the Animal Collective before their new album is a great way to start off.
Album: Strawberry Jam

Blonde Redhead - Equus - Good rocking song that shows off the singer's beautiful voice.
Album: Misery is a Butterfly

Deerhoof - Running Thoughts - One of the best tracks off their new album. It's hard to describe. The music all seems very american, but the girl's voice is obviously japanese. You'll hate it or love it.

The Go! Team - Junior Kickstart - This is a great track off their first album to introduce someone to. Their new album is also very very good. Very nostalgic, 70's inspired.
Album: Thunder, Lightning, Strike

Quasi - The Poisoned Well - This is when Quasi was still a great band. Give this a listen especially if you like Elliott Smith.
Album: Featuring "Birds"

Genesis - Watcher of the Skies. If you've never heard 70s Genesis, check this out. It's nothing like "Invisible Touch" or "Land of Confusion." The mellotron intro is so cool.
Album: Foxtrot (1972)

Yes - Roundabout. I'm still surprised when I hear people haven't heard one of the greatest songs ever created. The bass and the keyboards are what shine in this song. The hammond organ solo in the middle? Most kickass thing ever.
Album: Fragile (1971/2)

Comus - Song to Comus. Disturbing acid folk song about a monster raping a girl in the woods. The vocals are the creepiest part. Great, great music though.
Album: First Utterance (1971)

King Crimson - 21st Century Schizoid Man. It's very strange that a song like this was released in 1969; it's very distorted and heavy. The instrumental break is one of my favorites and the sax playing is excellent. Amazing song.
Album: In the Court of the Crimson King (1969)

That's enough for now.

All you music freaks probably heard this already but anyway:

Air - La Femme d'Argent - A pretty good example of their music, I think. Really mellow instrumental electronica, good stuff.
Album: Moon Safari

Audioslave - Exploder - Excellent song off their best album, IMO. You've heard Cochise if you played Guitar Hero, this sounds pretty similar. This is good old-fashioned ROCK, no sissy indie bullshit here.
Album: Audioslave

The Beatles - Strawberry Fields Forever (Love version) - Everyone should have heard this song by now but a lot of people haven't so there. It's an awesome remix from the Love album, I like it better than the original.
Album: Love

Brian Eno - First Light - This is reallllly ambient music, about the chillest music you'll ever hear, probably. Very minimalist, mostly piano. I actually haven't found too much stuff that sounds like this (I havent looked too hard but anyway) so if you have any let me know. Reminds me of Erik Satie a bit.
Album: Plateaux of Mirrors

Snoop Dogg - It's You I Adore (Sunshine) - I know Errors be blazin'
Album: Dr. Dre - Look Out for Detox

Easy Star All Stars - Electioneering (Radiohead cover) - This is probably one of my favorite cover songs ever. If you don't know about Easy Star All Stars, they're a reggae group who covered Dark Side of the Moon and just recently OK Computer. Both were fucking excellent and this song is my favorite of theirs.
Album: Radiodread

Jay-Z - Dirt Off Your Shoulder (Danger Mouse Remix - If you like rap at all, you've probably heard this by now, but this is an awesome remix. Basically this guy took Jay-Z's Black Album and mixed it with The Beatles' White Album. Results = awesomeness.
Album: Danger Mouse - The Grey Album

Shpongle - My Head Feels Like A Frisbee - I really can't listen to Shpongle unless I'm really high, but when I am it's great music to do stuff to, I especially love it when I ride my bike somewhere. It's very techno-ish but has samples from different styles of music, so check it out.
Album: Tales of the Inexpressible

Wolfmother - Joker & The Thief - You've probably heard these guys already or at least heard of them but I'm gonna plug them anyway cause I've been listening to them recently. They're a new band that plays old-school style rock, and they do rock.
Album: Wolfmother

EDIT: That Sweater song by mewithoutyou was pretty good.

I've only got one for now but...
Danger Mouse and Jemini- Omega Supreme
Danger Mouse and Jemini are definitely one of my favorite rap/hip hop acts. This is one of the many great songs on the CD.
From the album Ghetto Pop Life

Benevento/Russo Duo - Play Pause Stop - really good keyboardist/drummer duo

i'll probably have more when i get the rest of my music to my hdd later

It's also on the Richard D. James album, but it sounds pretty much the same except for the first few seconds. But yeah, this is my new ringtone, props for reminding me about it.