This is the unaccompanied song from the closing credits of The Disappearance of Haruhi Suzumiya (which I have just watched again in its entirety, and it's just as great the second time) , performed by Yuki Nagato's voice actress Minori Chihara. The song's Japanese name is romanised as Yasashii Boukyaku. I know that Yasashii means 'gentle', but that's as far as I get.
I am not sure of the correct English name for it, as there seem to be several attached to different videos, so just for the sake of having something in this post's title I have taken the one from this video.
It is a haunting theme, and stands as it is, even without English words and with just a still image of Miss Nagato throughout..