Well. Awesome. I love music that makes you feel like your chest will explode from the sheer power behind it. Some of the posts in this thread seem to interpret intense and powerful as "music I really like", which often doesn't actually fit well with those adjectives. So the below are not my favorite songs--though they're all really really good--but are certainly the most intense and powerful I can think of.
Let's see, as usual, it's hard to pick just one...
Listen to them all with the volume all the way up, and use a subwoofer if you have one! Shake your whole goddamn house!
Oh, and really anything by Hans Zimmer--Basically the entire soundtracks of Pirates of the Carribean, The Last Samurai, and Inception are fucking amazing.