I'm quite drawn in by the background music of
Hikaru no Go. It's so motivational, incredibly serious and very complementary to the slice-of-life literary genre that it's classified in, as well as to the very game [Go] that it does greatly in portraying. If it weren't for the music, I actually probably wouldn't be as in tune with it with my emotions as much as I am.
As far as opening or closing theme... It's my second favorite song of all time and it's the special ending to said anime series above:
Everlasting Snow by J-Pop all-girl group dream. It was used in the
Hikaru no Go 2004 New Year Special movie. Ah, how just beautiful sounding it is, and once again, something complementary, which does so to the actual closing sequence almost, if not, just, perfectly.