Stridone said:
If you like Sigur Rós, definitely check out Explosions in the Sky. 65daysofstatic is brilliant too.
Just as a warning, Sigur Ros shares almost nothing in common with either of these bands, especially 65daysofstatic.
Takk... shares the most similarities with them, but they are very different bands. EitS is awesome, 65days... not so much.
Check out Mum and Amina for more awesome Icelandic music. Amina were Sigur Ros' muse and they did all the string arrangements you hear throughout their albums. Mum is just a really amazing electro-pop-ambient (not the best descriptor of them, but it's about the closest thing to describe them) band that make some really diverse music. AVOID 'Go Go Smear the Poison Ivy', as it's only half of Mum and just bad. DO GET 'Yesterday Was Dramatic, Today Is OK' and 'Finally We Are No One'. If you feel adventurous (and I recommend this simply because I'm Icelandic and the album is hilarious), track down 'Blai Hnotturinn'. It's hard to find, but so worth it; it's the soundtrack they did for a play way back in 98 about a blue sphere and this Spider Queen who is at war with these Trolls, it's great. If you want more Icelandic music, check out Olviss, Jakobinarina, Gus Gus, Mugison...
Otherwise, check these duders out:
Kraftwerk
Brightblack Morning Light
Devendra Banhart
Vetiver
The Raveonettes
Serge Gainsbourg
M.I.A.
Lou Reed
Mice Parade
Do Make Say Think
Mogwai
Of Montreal
Shout Out Out Out Out
The Unicorns