Many of you have asked for videos from various games. I spent the last few hours putting these together for you guys. Hope you enjoy! Feel free to post any that I'm missing...
The 7th Guest
The 7th Guest 2: The 11th Hour
Advent Rising
Amazon: Guardians of Eden
American McGee's Alice
Beneath a Steel Sky
Beyond Good & Evil
Black & White
Blade Runner
Broken Sword: The Shadow of the Templars
Broken Sword 3: The Sleeping Dragon
Broken Sword 4: The Angel of Death
Conquests of the Longbow
Creature Shock
Cyberia
Cyberia 2
Darkseed
Darkseed 2
Dracula 2: The Last Sanctuary
The Dig
The Elder Scrolls III: Morrowind
Fallout
Fallout 2
Freddy Pharkas: Frontier Pharmacist
Full Throttle
Gabriel Knight: Sins of the Fathers
Grand Theft Auto: Vice City
Grim Fandango
Goblins
Gold Rush
Homeworld
The Horde (not related to Warcraft)
Indiana Jones and the Last Crusade
Indiana Jones and the Fate of Atlantis
Indiana Jones and the Infernal Machine
Indiana Jones and the Emperor's Tomb
Indigo Prophecy (Fahrenheit)
Innocent Until Caught
Keepsake
King's Quest 1: Quest for the Crown
King's Quest 2: Romancing the Throne
King's Quest 3: To Heir is Human
King's Quest 4: The Perils of Rosella
King's Quest 5: Absence Makes the Heart Go Yonder
King's Quest 6: Heir Today, Gone Tomorrow
King's Quest 7: The Princeless Bride
King's Quest 8: Mask of Eternity
Laura Bow: The Colonel's Bequest
Laura Bow 2: The Dagger of Amon Ra
The Legend of Kyrandia
The Legend of Kyrandia 2: The Hand of Fate
The Legend of Kyrandia 3: Malcolm's Revenge
Leisure Suit Larry in the Land of the Lounge Lizards (EGA)
Leisure Suit Larry in the Land of the Lounge Lizards (VGA remake)
Leisure Suit Larry 3
Leisure Suit Larry 5 (no on knows what happened to LSL4; expect Al Lowe)
Leisure Suit Larry 6
Leisure Suit Larry 7
The Longest Journey
The Longest Journey 2: Dreamfall
Loom
Maniac Mansion
Maniac Mansion 2: Day of the Tentacle
MegaRace
MegaRace 2
MegaRace 3
The Secret of Monkey Island
Monkey Island 2: LeChuck's Revenge
Monkey Island 3: The Curse of Monkey Island
Monkey Island 4: Escape from Monkey Island
Myst
Myst 2: Riven
Myst 3: Exile
Myst 4: Revelation
Myst 5: End of Ages
Normality
Quest for Glory 1: So You Want To Be A Hero (VGA Remake)
Quest for Glory 2: Trial by Fire
Quest for Glory 3: Wages of War
Quest for Glory 4: Shadows of Darkness
Quest for Glory 5: Dragon Fire
Phantasmagoria
Psychonauts
Return to Zork
Runaway: A Road Adventure
Sam & Max: Hit the Road
Simon the Sorcerer
Simon the Sorcerer 2: The Lion, the Wizard and the Wardrobe
Simon the Sorcerer 3
Shivers
Space Quest 1: Roger Wilco in The Sarien Encounter (VGA Remake)
Space Quest 2: Vohaul's Revenge
Space Quest 3: The Pirates of Pestulon
Space Quest 4: Roger Wilco and The Time Rippers
Space Quest 5: The Next Mutation
Space Quest 6: Roger Wilco in The Spinal Frontier
Syberia
System Shock 2
Tex Murphy: Mean Streets
Tex Murphy 2: Martian Memorandum
Tex Murphy 3: Under A Killing Moon
Tex Murphy 4: The Pandora Directive
Tex Murphy 5: Overseer
Thief: Deadly Shadows
Toonstruck
TRON 2.0
Ultima 7
Ultima 8
Ultima 9

Arrrrr! Darkseed still makes me shiver it does!
ps: Avast! It's Talk Like a Pirate Day!

Haha the 7th guest, what a classic :-)

Crusader: No Remorse
Crusader: No Regret
Wing Commander II: Vengeance of the Kilrathi
Wing Commander: Privateer

One of the best intros of all time:
Descent: Freespace - Intro Movie

The Witcher
Not sucking up to CD Project, but I think this is one of the better, more thought out intros of recent years. Such work that went into it. and it's genuinely interesting to watch.
I also love the Quake 3 intro. Pity it only ever ran once when you first launched the game (although the "com_introplayed 0" cvar would reset it), but it was a good way to get pumped up for a match :)

I remember playing that as a child. This game scared the hell out of me ;) I never got far, though, because I was just plain bad at adventures back then. Also, I think I had the English version, which didn't make it easier since I couldn't speak/read English.

Very good list! Here's few more
Dune 2
Syndicate Wars (One of my favorites. Almost like a short movie. ;) )
Dreamweb ... no words. *sniisk*
Day of the Tentacle
Privateer Lipsync nightmare. ;)
Those are my favorites.

These are cool too:
WarHammer 40,000: Dawn of War
Paraworld
StarCraft: Brood War
Not an intro, but still pretty awesome: StarCraft II trailer