Broken Sword 1 = Best game ever.
Grim Fandango I got about 1/4 of the way through, then stopped playing for some reason. Can't remember why, but I'll pick it up again eventually. Did the same thing with The Longest Journey; it was collecting dust for a year, until I started playing it again a few days ago.
As far as strengths and weaknesses go, I think adventure games are similar to many of the better novels and movies out there. Apocalypse Now, 1984, and Broken Sword are all extremely rewarding works of art, but they don't offer the cheap thrills that games in other genres, and comedies and action ("action" action) movies have. So I find myself watching Family Guy more often than reading or watching truly outstanding films, and, in the same vein, I play first-person shooters more than adventure games.
Another specific weakness is that adventure games aren't very social. Action, sports, strategy, role-playing and war games more often include multiplayer options, or at least make it easy to take turns with mates, whereas most adventure games pretty much demand that the player sits alone for extended periods of time with but his or her thoughts and a bunch of NPCs for company. That's fine for those of us who are rather introverted (e.g. me), but some people see it as "unhealthy".
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