I think the first adventure game I ever played was "Day of the Tentacle" - I still remember what you had to do to that poor hamster to this day. :D
"Sam & Max Hit the Road" was probably my all time favorite. Twisted, goofy, and a frickin riot. I'm glad that there are new Sam and Max adventures to play (am waiting for the complete set to come out and then get them all at once)
"Full Throttle" and "Grim Fandango" were also very good, as were King's Quest and Roger Wilco Space Quest series, of which I've played a several of the games and have enjoyed them greatly. Never did finish the Indianna Jones one, though for the life of me I can't remember why.
Recently I played an online one that was very good: "Nick Bounty: The Goat in the Grey Fedora". Graphics are a little odd, but it's got the same feel as the old Lucasarts games and has some very funny bits in there.
here's the link if you want to play for free.