This is one of those questions that simply cannot be answered with a single piece of music. Further, there are so many symphonies, concertos and operas that are awesome as complete works, but the bits and pieces aren't always equally great individually. So I'm limiting this to shorter pieces, a few of my favorites.
Stanley Meyers - Cavatina From the Deer Hunter soundtrack, and I love it.
Vocalise - Rachmaninoff So different from much of his other work, soft and gentle.
Debussy - Clair de Lune Gentle and powerful at the same time. I tend to prefer the "lighter" classical sound of guys like Debussy so this one really does it for me.
Swede