Oh, I still do love point and click adventure games. These days I mostly play freeware and flash-based ones. But they were pretty much the only games I played on the PC.
Shivers and Shivers II rank high IMO, because I always liked games with a creepy edge to them. 7th Guest and Myst were great (their sequels were alright too). I remember playing Clandestiny, which was humorously scary (and also done by the 7th Guest people), but not nearly as good as 7th Guest. I think I also liked 7th Guest and Shivers because the game disks also functioned as music CDs, so you could listen to the BGM and whatnot from the games. Shivers II's story focused around a band, so I listened to those songs alot. XD And 7th Guest's "The Game" is still a pretty good song to me.
There was Obsidian (weird but fun), and Titanic: An Adventure in Time where you played as a guy transported back in time to when he was aboard the Titanic, and he has the opportunity to prevent WWI, WWII, and one other war I can't remember. Educational and suspenseful! I was really interested in the Titanic at the time.
Bad Mojo was probably the first CD-rom game I played. While not technically point and click, it still fits in the whole puzzle solving thing. You're a guy who gets trapped in the body of a cockroach and has to make his way through his apartment building back to his body. You'd see some gross things sometimes (like a giant rat trapped in a mousetrap), and some moments were so scary and tense, like trying to get past a giant spider that would kill you unless you managed to use your tiny body to face a burning cigarette towards him so when he jumped at you, he ended up burning himself to death.
Loved Zork Nemesis. There was also a weird one called 9: The Last Resort, and had all the random celebrities voicing in it, like Cher, James Belushi, Christopher Reeves, and Aerosmith. Something about how your uncle (Christopher Reeves) had died and had left you his resort when artists and musicians would come to be inspired. I feel like the designers must have been high a lot of the time to make that game.
And probably the weirdest one of all, Bad Day on the Midway. You're at a carnival and can jump into different people's bodies and see their thoughts. The goal was to pick a person and try to get their to specific ending without getting murdered by the serial killer (you could play as him too), or dying from the Red Rat Plague that would eventually start killing everyone off. It was a rather disturbing game...
I did play Grim Fandango. It was alright; I don't know why I didn't love it completely. I played a bit of Last Express, but never quite got the hang of it.