I've thought about this a lot, too. What I've started to think about is that puzzles can actually be more of a problem than they're worth, particularly if they're very difficult, obscure, or unrelated to the story.

I see basically three distinct ways GAGs can be good. For one, they can focus on excellent stories, dialogue, and characters, like The Dig. The puzzles in these games should be minimal and not distract the player too much from the action. Furthermore, all the player's actions ought to relate directly to the story, to help further it. The Gabriel Knight series fits here.

A second type of GAG takes the opposite approach and emphasizes puzzles over all else. A good example here is The Seventh Guest, or perhaps more recently The Sentinel: Descendents in Time. These games erect a minimal story and characters and then put the player's focus squarely on solving largely plot-independent puzzles. If the puzzles are fun, then these games don't seem to suffer at all from the lack of a good story. I would put the Myst series in here as well, but with the qualification that those games tend to also focus very strongly on immersing the player in a virtual world. The "puzzles" are all based on learning about that world and how it operates. While there are stories attached to the Myst games (this comes out very strongly in the last game), I'd argue that what draws people to them are the intriguing worlds and the clever, often hopelessly abstract puzzles.

Finally, a third type focuses on irony and self-parody and thus tries to appeal to the player's humor. Sure, there may be characters and puzzles, but it's all tongue-in-cheek and seems to always be nodding and winking at you (nudge nudge). There are plenty of LucasArts games that fit this description (perhaps starting with Maniac Mansion and Zak McKraken), but also some Sierra games (particularly the Space Quest games) seem to fit as well. Another important characteristic is lots of allusions to stuff outside the game, such as American pop culture (Star Trek, Star Wars, Indiana Jones, other videogames). The idea here seems to be to focus the player's attention on the game's interface rather than try to immerse him or her into a coherent game world.

Ultimately, though, I think it's rather silly to talk about the "death of the GAG" when there's still a vibrant commercial development going on. Myst V just came out last year, sold very well, and despite Cyan's ridiculous statement, they're already working on URU (doing it the way it should've been done the first time) and probably even working up a new Myst game. FunCom just released Dreamfall, a sequel to its classic The Longest Journey, and it's met with some success (I'm actually playing it now, will review it soon). Meanwhile, Her Interactive's Nancy Drew series is the #1 videogame series for women, period. I also happen to enjoy them! (I've even read some of the novels that come with some of the games.) Finally, let's not forget the Adventure Company, which always has at least two or three new titles coming out every year, many from small-time or foreign developers. Some of these are extraordinary (I'd recommend Return to Mysterious Island VERY highly), while others are crap (Nibiru, Journey to the Center of the Earth).

Now, if we compare GAGs to first-person shooters, MMORPGs, and real-time strategies, yeah, they're definitely on the low-end. However, I'm not sure I'd want that situation to change. It's nice to have an alternative to the mainstream. I don't always want to see the billion-dollar Hollywood orgasm everytime I go to the cinema. Often, a smaller, less popular film actually has much more to offer my demographic (people with taste). :-) If a GAG only sells a hundred thousand copies rather than a million, so what? There's enough room in the market for that group, particularly if they stay faithful and keep buying new titles.