Grim Fandango
My jaw dropped for the entirety of this game, but it actually unhinged on these occasions:
Spoiler:
When Manny runs down from the Casino and see's Meche, but as he gets closer 'Meche' turns around, and it's a crow.
When Lola dies.
The poisoning at the start of the game. So weird.
When Meche is going through the gates with the suitcase of Golden Tickets, and the crow flies out at her... She hits it with the suitcase and then throws it down to Manny, and Manny get's into the car with Olivia, and then she throws Sal's head into the back of the car.... and he says, "Hola Manuel!". That part was also hilarious in a completely disturbed way.
The shoot-out between Manny and Hector. Awesome.
Full Throttle
Spoiler:
The entire end sequence of events, but one moment that stands out in particular is when Ben and Ripburger crash through the windscreen, and Ripburger is hanging on the front of the truck...
Mo - "Ben!? Ben!??? Are you alive?!"
Ben - "I am, but I don't know about Ripburger..."
Mo - "I can see him. He's out cold."
And at the precise moment she says, "Out cold!" we can see Ripburger's eyes shoot open, unbeknown to our heroes.
Metal Gear Solid
Spoiler:
This entire game was awesome, but especially the part where the mindreader dude makes the PS1 controller shake... and the torture part... they just added such an interactive element to the game, they were such clever ideas....
Monkey Island 2
Tunnels!
Probably there are a whole bunch of other moments, but those stand out in particular to me.