I think Lure of the Temptress was one of the first I did complete fully. Well worth it as there are loads of extra parts within some of the scenes that only get unlocked, or make sense towards the end. It was also the first game to try and introduce a real-world feel to characters, using their Virtual Theatre system.

One thing I always liked about the good Adventure games is that they removed the "level" feel to them as you moved around the screens like a virtual world.. these were in a way some of the first open world ideas, but with a fairly linear main story.

You also can't discount Flashback, although that was more an Action Adventure with some RPG elements, especially the middle of the game where you had to get a job and spend ages working and running errands to earn enough money to enter the game show to win the ticket to Earth.