In terms of powerful soundtracks, Hans Zimmer's score of The Lion King is usually the first to come to mind.

As a kid, it was the first soundtrack that moved me to near tears. I was less interested in the vocal songs (to be fair, I still love them) and found myself drawn to the orchestrations.

When I got older I learned that Hans' father died when he was a kid and that he was able to bring a personal touch into the score, and it showed.

To answer your question, the most powerful soundtracks that I can think of paint a clear picture or emotion (or at least a few interpretations of them). For instance, the song "The Illusive Man" from the Mass Effect 2 soundtrack gives me feelings of power with a sinister undercurrent.

Illusive Man Theme: https://www.youtube.com/watch?v=UBLOvSb56Vc

This Land (The Lion King): https://www.youtube.com/watch?v=TGDXTZFleHQ