Songs range from ambient to post rock to acoustic rock to nearly heavy metal
Very original arrangements
Non traditional instrumentation (e.g. vibraphones and guitars played with cello bows, lots of interesting percussion, lots of sampled sounds, bass guitars played with drumsticks, etc, all lend themselves to a very unique sound)
Songs have a linear quality to them, they are mostly divided into movements rather than verse/chorus/verse/chorus
Lead singers voice is just incredible - soaring falsettos that last for 30+ seconds at a time in some cases, also, sings in Icelandic which is good if you need to use it as background music for studying or just want to hear something unique
It's just really interesting stuff - some people might think that is a turn off because they say 'experimental music sucks because it deviates from tried and proven formulas of pop' but SR is able to combine these experimental bits with rock/pop bits and make it work.
Sigur Rós - Hoppipolla (one of their more easily digestable songs)