Ahhh, Flashback. I can still see Conrad Hart's jacket billowing out as he makes a sudden change of direction. That spent
years at the very top of my favourite game list.
On topic (I'm trying bysmitty
):
Beyond Good and Evil - for the wonderful character development.
Thief series - for the story and atmosphere.
System Shock 1/2 - ditto.
Prince of Persia: Sands of Time - for making you think a bit (and for the character development and story).
and Flashback's predecessor,
Another World - which was even more Adventurey than Flashback.
I'm also guessing
Psychonauts is a contender but I'm yet to play it.