Great Instrumental rock bands/albums?

You should try the song "Regatta de Blanc" by The Police. They're not an instrumental rock band, but that song is my favorite instrumental of all time. Best drummer in the world!

@McGhee_the_Insomniac said:

TOE from Japan. Possibly the best band in the world.

Yeah, definitely check out Toe.

Piglet, Giraffes? Giraffes!, 65daysofstatic and Battles. 
 
Errors and Three Trapped Tigers are also  good but they're more electronic than rock 
Edit: I'd definitely recommend Brontide as well

Explosions in the Sky
Do Make Say Think
Godspeed You! Black Emperor
Mono
Tortoise
Red Sparowes
Meanwhile Back in Communist Russia...
This Will Destroy You
Gregor Samsa
Yndi Halda 
Broken Social Scene  Ok, here's a few that come to mind.

If These Trees Could Talk. A shortened version of Malabar Front was used on the Infamous trailer, but they're first EP and their first LP were fantastic stuff, looking forward to mor by them. 

Blotted Science comes to mind.

Natural Snow Buildings

I'm such a sucker for anything labeled "post-rock"
 
God Is An Astronaut is great
 
  

Acid Mothers Temple

Giantbomb I am disappoint
 
And So I Watch You From Afar, awesome Irish band
 
      

Try out The For Carnation and Mono.

Dirty Three,Cinematic Orchestra and Pelican are the only bands I can think of that I don't think have been listed yet.

Explosions in the Sky
Do Make Say Think
Godspeed You! Black Emperor
Mono
Tortoise
Red Sparowes
Meanwhile Back in Communist Russia...
This Will Destroy You
Gregor Samsa
Yndi Halda 
Broken Social Scene  Ok, here's a few that come to mind.

Don't know if this has been mentioned: 
 
  

@FancySoapsMan said:

Explosions in the Sky
Do Make Say Think
Godspeed You! Black Emperor
Mono
Tortoise
Red Sparowes
Meanwhile Back in Communist Russia...
This Will Destroy You
Gregor Samsa
Yndi Halda 
Broken Social Scene  Ok, here's a few that come to mind.

Jesus Christ.  We like all the same stuff.  For some reason I'm a bit surprised that someone else knows who Gregor Samsa are.

Maybeshewill

And So I Watch You From Afar

Red Sparrows

65daysofstatic

Talons

You Slut!

but this is probably my favourite instrumental song ever, not normally an instrumental band, but i think it desearves a mention

There's this whole website, The Silent Ballet, that reviews only instrumental and experiment post-rock bands. Perfect!  
 
I think Yndi Halda is my top favourite out of all the bands mentioned here (bought it, thank god it's a sleeve instead of those fugly plastic jewel cases). A few facts I've noticed: quite a few Texan bands. Everyone references Explosions in the Sky. Hard to buy them for an official CD release (at least here in UK), most are MP3 albums.  
 
And no one has mentioned Samuel Jackson Five (#1 album of 2005) yet: 
  

One more fact: World's End Girlfriend is the most experimental band in this genre, and hard to classify since it's just one guy fucking will all kinds of instruments. 

Explosions in the Sky, Godspeed You! Black Emperor, and i'm not sure if it fits but Flying Lotus.

I dislike how quickly these threads turn in to "spam shit from youtube that you think is cool" threads. But I will highly recommend that you check out John 5. What he does is mainly guitar stuff - the guy can riff. Mostly rock, with a touch of bluegrass here and there.

Explosions in the Sky.