To be honest, I think this thread isn't specific enough because its not clear about whether or not by "intense" and "powerful" you mean music that proclaims that someone is all-powerful or an epic hero, like most everying by Two Steps from Hell ("Heart of Courage" is a prime example of why I like them.), any song by Dragonforce (I like "The Last Journey Home."),
or emotionaly intense or powerful like "My Immortal" by Evenescence, most songs involving love sung by Josh Groban ("Remember When it Rained" is my current favorite.), or the love theme from Dragon Age,
or situationaly intense or powerful like almost any final boss music anywhere (Like "The Greatest Jubilee" from Bayonetta), a movie soundtrack (like the music from "Star Wars" by John WIlliams), or a song about death/doomsday/insanity (like "One" by Metallica),
because my answer will vary depending upon what you are talking about, and since this list is too large I cannot post links and is forced to pray that everyone here knows that Youtube hosts music too,
but I can have an excuse to place one of the largest sentences ever used in an internet forum for kicks praying that somebody has noticed that despite the spaces this is still one long sentence with a ton of commas.