Now the first thing I do when I find a new group is I check out Wiki, so . . . here's their entry. The main reason i do that is so that I can see with their music is available. There is nothing worse to me then hearing a song, love the artist, and then finding it impossible to find more of their music.
So, Sigur Ros . . . A friend Facebooked (is that a real verb?) one of their videos, Viorar Vel Til Loftarasa, and almost immediately I became addicted. Jón Þór "Jónsi" Birgisson's voice grabbed me, emotionally, and wouldn't let go. It is worth mentioning that Jonsi also has a solo career, which is worth investigating as while.
A few things about the group. . . Jonsi identifies as Bisexual, the group is very GLBT friendly, and if you want to check out Shia LaBoeuf's hot naked body doing ballet type dancing and cross dressing, check out their video, Fjogur piano . . .
Sigur Ros currently has 6 albums, all in Icelandic, all emotionally vulnerable, so check them out. I guarantee you won't regret it.