I liked when Peach was falling from the airship and Mario saved her. But the one I like more is the intro with Bowser stealing the castle and Rosalina transforming the spaceship in a comet.

Maybe not a cutscene, but more like a secuence: Link and Zelda escaping from Ganon's Castle in Ocarina of Time.

Such an atmospheric game, and such a step up in scale from the last two.

Someone already posted the Chapter 12 one, so I'll post this one.

In Paper Mario: The Thousand-Year Door when The Shadow Queen became invincible and all hope seemed lost. All of the friends you made along the way cheer you on and give you a resounding sense of hope and courage. It was just beautiful and climaxed the second greatest adventure game I've ever played. I even got teary-eyed.

Maybe not epic, but still linger in the memory:

Oh, and this one.

Depends how you define epic.

These two:

The Interloper cutscene from Legend of Zelda: Twilight Princess. At first I thought it was just weird and creepy, but later I realized that for those that pay attention, this scene contains a lot of symbolism. It's very well made artistically and the scene is basically the definition of the tone of the game. Twilight Princess actually contains many great cutscenes. I'd give the honourable mention to the Ganondorf's execution scene at the Arbiter's Grounds. 

And 'Revan's Revelation' from Knights of the Old Republic. This video includes the lead-up and the aftermath, but I think those should be included to understand the full context. Darth Malak's monologue is quite essential. When I first saw this scene, it completely blew my mind. How did I not see? All the clues were right there, as flash-backed by the cutscene. I am Revan, and I never knew! Utter brilliant game story wrinting, and one of the best games ever made overall. There's just two things EA could possibly do to make me buy a game of their's again, one of them is letting Bioware make a KotOR 3 that's as perfect as this one.

The inFAMOUS 2 good ending cutscene was pretty epic

http://www.youtube.com/watch?v=Rh31AGbHfRs

for me its this scene from Heavy Rain which had a big impact on my emotions tbh

http://www.youtube.com/watch?v=J9K_T_klwRQ