First of all, sorry if this is lame, but I need to find something new to listen to. I've been searching the web for new bands (or at least some that I am currently unaware of) but I can't seem to find anything that catches my attention. I want something that sounds unique, but everything so far is meh.  So I want to turn to the Giantbomb community for some good original bands.  Here is some info about my tastes to keep in mind:
 
 - Nirvana - Kurt Cobain was an amazingly talented song writer. The music and lyrics  are dripping with sarcasm and angst, no one does it better.  They also had great  B-        side/rare songs  
 - The Beatles - obviously 
 - Songs that are "quietly messed up,"  if that makes sense. 
 - The Dark Side of the Moon -  speak to me, Breathe,Time, Money, - YES  
- I kind of like that  Make War song by Bright Eyes , though I feel bad about it for some reason.
- Nine Black Alps' first album was cool. 
- Gorillaz - El Manana , Feel Good Inc, etc.
-Things that suck - Metal, John Mayer, Pearl Jam (sort of), Linkin Park
 
Any suggestions?

PISSED JEANS (that's the name of the band)! If you liked Nirvana you should like King of Jeans. That's their latest album I think and it's pretty nice.

Well, Radiohead is the first thing that pops into my mind, but you probably already know whether you like them or not.
 
Joy Division fits nicely into your "quietly messed up" category, though given that the lead singer hung himself I don't know how quiet it really is. 
EDIT: Its better if you don't watch the pics in thsi video.
 
 

Well, it seems like you are mainly a rock kind of person. I've been listening to nothing but rap for a while now, but maybe I can look at some of my older music and see if I have anything you'd like. 
 
I'm just grabbing random stuff from itunes... 
In the past, I've really enjoyed: 
Nine Inch Nails 
The Offspring 
Cake 
Reel Big Fish 
Flogging Molly 
Sublime 
Mindless Self Indulgence (I really liked them, a lot of people don't) 
Xavier Rudd (Some great chill music) 
 
Upon further reflection, I think you've probably already heard of all of these bands, but I'll bring them up just in case. It feels weird suggesting this type of music to someone, because as I said, I've been mostly into rap lately. If only you had asked for my favorite MC's. 

Cake!!!!!!!!!!!

" Cake!!!!!!!!!!! "

Bands to check out that are chamber pop esque  
 
Belle and sebastian 
The decembrists 
I'm from barcelona 
 
Bands to check out that are Hard rock 
Evans blue 
parabelle 
 Brandnew
 
Bands to check out that are kind of in there own catagory 
Twilight sad 
 POLYSICS
(these bands sound nothing alike) 
 
Hip hop 
 El-p 
Aesop rock 
atmosphere 
 the roots
i also agree with the dude that said Joy division and the smiths and will also add the cure and echo and the bunnymen

I agree 100% with everything that Mr. Skeleton said (except the bit about Queen, but thats just me).

Hey I would say try:
 
The Republic Tigers
Wilco
Depeche Mode
Phoenix
ELO

Natetodamax and Metal Gear Sunny might like me for listing these bands just for you!! Lol.
 
Foo Fighters
Queens of the Stone Age
Them Crooked Vultures

Queens of the Stone Age. Every album is different, so if it's not your thing take the time to check out their others.

Oh man, if you have only started with radiohead you have many hours of sheer musical exstacy ahead of you.
 
These guys are nice and dark:
 

Have you ever listened to Phish? 
I also like this band: http://www.myspace.com/stonefeathermusic

You should try Eatliz, they are an amazing israeli indie band. 
      

Also a few other songs you might like (most of this list leans toward heavy rock but you might like it):  

http://www.youtube.com/watch?v=051VhDUyras    

ttp://www.youtube.com/watch?v=WEQnzs8wl6E       
http://www.youtube.com/watch?v=bKttENbsoyk       
http://www.youtube.com/watch?v=Y0LuFaPtmt8      
http://www.youtube.com/watch?v=wS7CZIJVxFY  
http://www.youtube.com/watch?v=5roz5-wdjBg

http://www.youtube.com/watch?v=14qTXRkAKr8      

http://www.youtube.com/watch?v=Rwc8dRM-zd0      

http://www.youtube.com/watch?v=WElvEZj0Ltw

  Ok, lets go for another one. My Nirvana obsessed bandmate loves The Replacements, and we do a cover of this song. I wish I could find the album version, it's a beautiful bit of music.

" Natetodamax and Metal Gear Sunny might like me for listing these bands just for you!! Lol.  Foo Fighters Queens of the Stone Age Them Crooked Vultures "

Thanks everybody!  I will definitely look into these.

you already got too many recommendations so i dont wanna stress you and add 10 items to your already-stuffed list

" Queens of the Stone Age. Every album is different, so if it's not your thing take the time to check out their others. "

Kyuss.