These were my favorite games as a kid.
They were fairly open-ended in that you could explore all of the environments which always appealed to me. Additionally, since they relied on using your mind versus your reflexes you could play them with a group of friends --- each person offering ideas as to how to solve the puzzles. We had the collection that everyone is referring to at the day care center I went to as a kid, and one summer all the guys huddled in the computer room and beat Last Crusade together.
A second collection came out which bundled Day of the Tentacle, Fate of Atlantis, the Dig, Sam and Max and I believe a demo of Full Throttle as well. These games featured better animation and full speech, but that first collection retains a special place in my heart.
Thanks to a great program called SCUMM you can still play these games on your mac and pc! I still have most of the original disks but you can also find them on amazon as well. I try to play through at least one each summer just to remind myself of those carefree childhood days