A computer game where you are in charge of one character, usually someone who has to go around solving a mystery by talking to people and examining their surroundings to find clues. Generally very linear games, which is the main complaint by people who aren't adventure game fans.

My favorite adventure games, in no particular order:
Police Quest
Sam and Max Hit the Road
Space Quest
King's Quest
The Secret of Monkey Island
Blade Runner
Blue Force
Full Throttle
Day of the Tentacle