Hard question. You have to ask what makes a game genre relevant. Personally, I play games for the experience. If I play a racing game I want to feel that I'm driving. If I play a shooter I want to feel that I'm in some sort of armed conflict and so on.
In that vein, Adventure Games are about going to places, meeting characters and getting involved in the story. If the places/characters are interesting the game is potentially -keep that in mind- good. With Tim Shaffer, those two elements are 100% guaranteed.
But interesting places/characters are just part of the equation, you also need to have game mechanics that complete the experience. This is where the challenge for adventure games lies. The point-and-click mechanic is quite limited; last time around, towards the end, designers were pulling their hairs out trying to come up with something new within those confines. Adventure games are inherently puzley; how many memorable puzzles can you possibly come up with?
I get the feeling that, as much as I enjoyed those games back in the day, their time is done. Double Fine Adventure (of which I'm a supporter) will function a lot on nostalgia, and probably will not revive the genre.