Here's one from one of my favourite bands lately, Porcupine Tree. Hard to find all their vids on YouTube, I'd highly recommend downloading them if you're into amazing prog rock. They do have a bit of a harder edge than this song too
A stunning instrumental by Radiohead that not everybody has heard. Good under the influence on a good system
I've gotta echo a bunch of the previous choices in this thread. Never have I had my spine tingle so much as at a TOOL concert. Radiohead and APC were good choices. My Weakness by Moby is stunning.
As I got into some heavier stuff this band produces some of the most mind blowing songs (Opeth). Almost everything by them is amazing for me.
The most beautiful Muse song
Portishead is one my favourites that hasn't been mentioned so far. They have an amazing live disc called P:NYC
Surprised I didn't see any mention of Massive Attack. One of my favourite bands right after high school. I played their album Mezzanine in my car for a year straight and it remains on my desert island list.
I might update this again or post more. In the Light by Zeppelin or Ten Years Gone is another goodie.