The first thing that occurs to me, in general, is the humor in many of the games, particularly the Lucasarts games that I love.

People actually have something interesting to say. The interaction with the environment.
The actual exsistance of humor.
A game that doesnt take itself too seriously is a lot more fun than one than that tries to be an epic war movie or something.

I think the real reason I have a soft spot for so many adventure games is that I adore the characters. Character design might not seem like such a big deal to many gamers, but I'm generally a very character-oriented person when it comes to any kind of media. Adventure games seem to have better defined characters than a lot of other genres (it certainly helps that talking and interacting with other characters is often a huge part of the game).

Most of my favourite computer game characters are from adventure games. They have in-depth personalities, some have clever backstories, and sometimes they will go through some character development as the game progresses. I just love them!

There are of course other reasons I like adventure games (some of which have already been said) such as the quality of humour, interaction with the environment (and the whole exploration side in general), the story unfolding while you play, and - in the majority of adventure games anyway - no dead ends, so you can be as experimental and silly as you want without worrying that you're going to make it impossible to finish.