I think that's the crux of it. You want the game to be challenging, but not frustrating. The problem with most adventure games is that they quickly get more frustrating than fun. Once people get stumped and frustrated enough, they just decide that genre isn't for them and move on to something else. Sadly, even the best games of the genre tend to have a few of these spots. In my opinion, they're still outstanding games even if you have to peek at hints a time or two, but if you're constantly having to consult them it's a bad design.

That's why I think the "younger" adventure games are some of the best, such as the Nancy Drew series. There the developers have ensured that there are enough clues to get you through. When you get bogged down, you simply have to dig deeper into your clues; you'll almost always stumbled upon the right solution. The games are comfortable to play because you know you're unlikely to get so stuck you have to consult websites. The puzzles are also fun, so it's not like it's so easy you won't be challenged.

I think the ideal developer would follow Ron's advice (see below), but in particular I'd try to anticipate problem areas and make sure there's enough in-game hints to get you through. If a gamer is just too lazy to explore thoroughly, fine, screw him. However, if players are performing due diligence, throw them a bone, geez. I think the CSI game I'm playing now is pretty smart; you can get hints in-game, but it "shows up in your evaluation," whatever that means. That encourages you to get through without hints, but they're there if you get too stuck. Lovely idea.