There's a really nice (lengthy) article over at Adventure Classic Gaming that takes a look at puzzles in (as you can probably guess) adventure games, and how those forms have seeped into other genres.
The in-depth look at a variety of puzzle forms moves from the premise that puzzles are so integral to adventure games, bad ones can easily ruin a game:
Adventure games are different—in that the core features of gameplay cannot be effectively evaluated without actually playing it or giving so many details away as to detract from the experience of playing the game. In many respects, the quality of an adventure game depends upon the quality of its puzzles, whether they are ingenious and rewarding or just frustratingly illogical. Having been told an explanation to how a puzzle works means you will never be able to play it as intended, since a big part of the experience is the enjoyment of figuring it out for yourself. You can evaluate the art, voice acting, and even the story or humor present in an adventure game to a certain extent without diving too deep into it, but an adventure game with terrible puzzles can make all those other elements irrelevant, since you likely will never have the patience to finish the game in the first place.
In this article, I will be taking a closer look at the various types of adventure game puzzles, how they relate to the gameplay, and even how some of these basic forms relate to other game genres.
From two basic classifications ('self-contained' and 'key'), a wide variety of puzzle types appear; the analysis is interesting and the article is worth plowing through if you're interested in the nitty gritty of game design.
Adventure game puzzles: unlocking the secrets of puzzle design [Adventure Classic Gaming via GameSetWatch]