if you aren't looking for the classical point and click adventure game,

I would support the comment above, Dreamfall The Longest Journey is surely one of the games you must check ,

and also Telltale's The Walking Dead Serie and Quantic Studio's Indigo Prophecy. I think these 3 are pretty much the best around..

If you look for more classical there are

Telltale's Back To The Future Serie which I really liked and Sam & Max which is very humoreous.

Harder games which you must play ,

The Longest Journey(1999) And Grim Fandango..