I've always loved this intro it has style and cool action with impressive effects considering the time it was made, though I'm not a cg fan anymore. Very Terminator 2 inspired with the slowmo turns and running away.
This one as well always left an impression on me and in my opinion fit best with what Battletech could be, and even should be at times, especially in the Innersphere. Just cutthroat ruthlessness with so many factions and powers at play. I love Mechwarrior 5 mercs but the tone is sadly way off and the few crew we get are obnoxiously ignorant and arrogant arseholes at times. Like no shit war is bad, but getting paid enough to survive and not get double crossed or rooked is paramount to survival. Great game but needs some work bigtime to really reflect the game universe. It really lacks in mission diversity or complexity sadly. Still love it though.
This one was always a fave too with my Sister and I, being fond of Star Trek and whatnot. I really loved the Narrator.
In terms of sheer industry impact, Metal Gear Solid. Right up until the end of the elevator ride, Metal Gear Solid's opening is simply incredible. In fact, Metal Gear Solid is largely responsible for the "cinematic movie game" trend we see dominating specific platforms today.
In terms of my personal favourite cinematic introductions, I'm going to go with Final Fantasy VII. By the time the logo and musical sting lands, you know you're in for one hell of a game. Magic, metal, sci-fi; it creates an incredible impression that I love to enjoy everytime I replay the game.
Man, I remember the time I found out about Policenauts, and discovering footage from the game. It was like finding long lost buried treasure. This part of the intro where the music kicks in with vignettes of Old Los Angeles 2040, my god cold chills.