Anathema - "Everything" has had me in tears more than once - mostly thinking about how I got to where I am, and particularly the family I've been blessed with.
Redemption's Snowfall on Judgement Day has many moments that really connect with me. So does Neal Morse's One.
"Jupiter" and "Neptune" from Holst's Planets for completely different reasons. Jupiter because of the immense beauty of the melody in the middle of the song, and Neptune because it awakens my curiosity of space beyond the solar system - every time I hear it I spend the next several minutes completely daydreaming what it would be like to fly out past the far reaches of the sun's influence (if it were possible).
Finally, "O Magnum Mysterium" is such a personal song for me. The vocal arrangement is simply phenomenal.