20 is The Secret of Monkey Island?
As guessed by The_Liquid_Laser, my first entry in the TOP 20 is The Secret of Monkey Island.
You play Guybrush Threepwood on his quest to become a pirate. What nobler quest there is. In the end he has to deal with the ghost pirate LeChuck and tries to win the love of governor Elaine Marley. All the way you solve puzzles that often in itself hilarious. Someone remembers the solution to this?
The probably most remembered part is, that Guybrush learns sword fighting, but get told the most important part is insulting the foe, so you can strike him hard.
The game also has memorable and funny characters. For instance Stan the salesman, which came back in future games in the series.
The game was designed by Ron Gilbert (again), in cooperation with Max Schafer (I mentioned them both with the text for The Cave). The game is part of what made LucasArts adventures the greatest back then.
There was a remaster some years ago with updated graphics, that have an artstyle I don't dig, but you can switch to the original graphics.