This is so tough because some of the classic games that I would say everyone should play just don't hold up graphically to todays standards. So here goes with my favorites:
1. Gabriel Knight 2 The Beast Within
2. Discworld 1
3. Discworld 2
4. LeChucks Revenge Monkey Island 2
5. The Longest Journey
7. The Black Mirror
8. Curse of Monkey Island Monkey Island 3
9. Broken Sword 1 Circle of Blood
10. Simon the Sorcerer 2 The Lion,the Wizard and the Wardrobe
11. Day of the Tenacle Maniac Mansion 2
12. Legend of Kyrandia Book 1
13. Secret of Monkey Island Monkey Island 1
14. Simon the Sorcerer 1
15. Runaway A Road Adventure
I also want to list the games I left off since they are older and not up to the graphic standards of todays games. These games might be older but they are well worth playing if you have missed them.
Zak McKracken and the Alien Mindbenders-
The Dig- Excellent music and atmosphere.
Tony Tough and the Night of the Roasted Moths
Challenging puzzles and funny voice acting.
Grim Fandango- A classic.
Fable- Short but fun.
Kings Quest 2- An oldie but goodie.
Kings Quest 7- Sierra games were always fun.
Dracula 1 & 2- I especially loved 2.
Space Quest Series- Monkey Island/Discworld
humor mixed with wicked puzzles.