Bagasaurus. No, really. I must have been, I don't know, two or three. I don't think this really counts.
The first games I remember playing with or watching my parents finish were either LucasArts titles like Loom, The Secret of Monkey Island, and Indiana Jones and the Last Crusade, or Sierra titles like Spacequest and King's Quest. The employee of the week at Monolith Burger in Space Quest III was an early, early memory.
I was playing computer games before I was really clever enough to finish them. The classic adventure ones, anyway. Then there was the Super Solvers series by The Learning Company. I'm not sure if I really 100% these, because the gameplay loops infinitely I think, but I definitely got through them. I think the first classic point & click adventure I finished was either Day of the Tentacle or Sam & Mix: Hit the Road.