The scene in TR3 with the bell-tower Geordies will always be a big favourite of mine.
And no matter my opinions on the game as a whole, the scene in FFX where Yuna 'sends' the lost spirits of Kilika to the Farplane is probably still the single most beautiful FMV sequence I've ever seen. This game is FIFTEEN-fucking-years-old. FIFTEEN.
Saints Row games always have fun cutscenes. The 'This Is How We Do It' ending scene, the Armageddon piss take, and playing Gat Out of He'll right now which has just done a big musical number with the Devil and his daughter!
Psygnosis always had my favourite intro's to games back in the day; they didn't make the best games sometimes, but they always had style.
The Killing Game Show, I remember seeing the intro for it and would not stop watching, I hadn't seen anything like that before. It looks slow and cheesy now but it was extremely impressive for 1990 :
This competes well with the woeful voice acting in Rez Evil 1 (which is still fabulously awful after all these years!); Blood Money :
Shadow Of The Beast, which was quite muted for an intro by Psygnosis with just a couple of pics, but the first time I saw it, I was at a mates house who had its music blaring out in surround sound, and it only helped increase the atmosphere and my now nostalgia for the game. I think a remake is coming out for it as well :
Finally, Wipeout, with those 120bpm beats, Prodigy score and a heck of a fine game to boot, I had my own surround sound for this by then :