I was wondering about the dope’s favourite cutscenes.
One of mine is this one from Final Fantasy XII: (Spoilers, obviously)
While it’s intwined into the story as a whole, I think it’s also understandable when you don’t know about the rest of the game.
I like all of this; the writing is excellent and the voice talent (coming from a theatrical background, I believe) really shines.
Other favourites?
I don’t have a link, but I always liked the Introduction of the Flood in Halo, by way of a soldier’s helmet cam video.
Dragon Age: Origins
The darkspawn overrunning Ostagar. I get a grin at about 1:24. A truly epic battle.
Metal Gear Solid. The first one. It’s been ages since I’ve played through it, but a few still come to mind: Sniper Wolf’s death scene made me cry. Psycho Mantis’s was also good. And let’s not forget our introduction to Revolver Ocelot. “This is the Colt Single Action Army, the greatest handgun ever made. Six rounds–more than enough to kill anything that lives.” And another Ocelot classic, from the torture chamber: “No turbo–I’ll know.”
I only played through MGS3 once, but it had some classics as well, involving young Ocelot.
2 and 4… well. The MGS series seems to be the mirror image of the Star Trek series when it comes to sequels. Most of the cutscenes in 4 seemed to be 40 minute powerpoint presentations… 
(Oh, and um, the like two cutscenes that involved Freya Crescent in FF9. Cause… um. I’ll be in my bunk.)
Oh! Not exactly a cutscene, but the opening to Star Ocean: Till the End of Time. Star Ocean: Till the End of Time Opening Movie - YouTube
Never finished the game, but the opening… it gave me chills again watching it right now. It’s sort of a sci-fi wet dream: From our first tentative groping beyond the atmosphere, through the space shuttle… and then into the great future that I feel ought to be our birthright, but probably never will be, between the laws of physics and our own timidity. 
From Homeworld, the Return to Kharak scene;* “Kharak is burning”*.
The Lady of Pain from Planescape: Torment.
From Thief 3, the intro clip for the Hammerites.
For something funny, there’s this from Alice: Madness Returns.
The big reveal in “Knights of the Old Republic.”
…I just love the dancefrom Final Fantasy Eight. Its just so nice. 
Honourable mention to the openingof Final Fantasy Seven. The first time I played it it blew me away and sucked me into the game.
No link, but I remember being enraptured by the opening credits cutscene in Assassin’s Creed 2. It’s not the very first thing you see, I’m referring to the quest early in the game where you climb to the top of a cathedral in a race with your brother and synchronize your first viewpoint and it gives a beautiful pan over Florence with the leitmotif for Ezio’s family.
ETA: Just found it on youtube, I remember there being a long panover, maybe I’m thinking of a different scene.