Well there's really too many games to list... But heres a few.
Little Big Adventure - Because it was my first PC game. I had seen another person playing it before and was in awe of it at the time. Then got my first PC and this was the first game I played on it. It wasn't the easiest game for my first time on a keyboard game because it starts off with you trying to break out of prison with plenty of guards to keep throwing you back in your cell. I loved the world and its creatures, the music was fantastic.
Quality FMV games such as Black Dahlia and Gabriel Knight 2 were interesting. But the Tex Murphy series is my favourite by far. Mainly because of the amiable flawed main character with alot of wit and resourcefullness. The world again was fascinating and atmospheric. I highly reccomend these games if you haven't already tried them. The Pandora Directive is said to be the better of the series.
Check out this website too:
http://www.unofficialtexmurphy.com/
Many Adventure games e.g. most of Sierra's line... I miss those days (Monkey Island series, Space Quest series, Freddy Pharkas Frontier Pharmacist, Sam and Max, Leisure Suit Larry etc.)
As Echolyn said, if Final Fantasy 7 can be counted I would also highlight that one too. It was the first game I played on the Playstation and I guess I don't need to go into how much I enjoyed it since its obviously talked about enough already.
Jam it back in, in the dark.