IMHO they are the most influential, creative band in the world (that I've heard). I was a little worried during their Limbs period (they got lazy I think), but Moon Shaped Pool revived my total trust in their incredible vision. That album took about 20 listens to get right, but boy, what an album!!
I was turned on to them by my oldest son. back in 2003, just after Hail To The Thief was released. Mike had given me Amnesiac as a gift years earlier and I couldn't get it at all. After a two day car trip where we played HTTT multiple times (along with OKC) the light came on...and has burned bright ever since. When I got back from that vacation trip I immediately soaked up Amnesiac, then Kid A, etc etc. They've been in my rotation ever since. We saw them at Bonnaroo in 2006 and then again locally in 2008 or 2009.