@Oddball:
What works and what doesn't work?
In my opinion, combat doesn't work in this kind of games. Not that it's completely off, but it's often poorly done by non-specialists and it shows.
Or you put combat in its most simplified form, like "Use Sword on Monster" and kill it.
I kinda remember now the Quest for Glory series had combats that weren't too badly done, but they weren't my prefered parts. I recently tried a remake of the first and constantly died during the sword fight tutorial... Well, maybe it's just me here
In general, action sequences (ie. anything that requires reflexes or skill) don't belong the Adventure game genre.
They are rather slow games, not very interesting to follow in a Let's play because most of the "magic" is in the story and dialogues, and that is a personal reaction for each player.
I'd call To the Moon an adventure game, because of its emphasis on dialogues. Take out the story and dialogues from this game, and you have nothing left.
Ever watched a Let's play of this game? It's often boring because the Youtuber tries to go fast and keep his audience entertained. You end up with a game that has no action and the magic of the story/dialogues didn't have time to work either. Total failure. An action-oriented game is more fitting in my opinion.
What works? There's no definite answer as there are different sub-genres and they appeal to different players.
For example, you have strong logic puzzles, like Myst. You have to take notes and think. And think hard sometimes.
Another kind of game is the Lucasarts style, with the Monkey Island series for example. Almost no logic here in the puzzles, they were made to be completely crazy and amusing because their answers were unexpected. A more recent example is the Deponia series, especially the last episode. Some people love it, I'm glad I only "played" it through a Let's play video.
I already mentionned To the Moon. It's a story heavy game. You could call this sub-genre a "visual story". There's almost no interaction with the world. You only click to start the next dialogue.
A more "classic" sub-genre if I can say so is the Blackwell series. They are very good games, with a story, dialogues, puzzles and interaction. They're a good example of a classic combo that works great.
I can also mention the text adventures, that rely only on... text. Sometimes with minimalistic graphics. It's often related to the "Choose your own adventure" books because of that.
There's also a sub-genre that may be linked to adventure games, that is Visual Novels. It's a story, sometimes with interaction/choices, sometimes nothing but illustrations for a on-rail story. Winter Wolves has tried to put more on the table with their games, and some of them are really good.
And many other sub-genres, no need to mention them all.
They all have games in their own categories that worked and others that didn't.
The most common point is that they have a strong story and memorable characters. Puzzles, unless they were very bad, don't stay in the players minds afterwards.