Yup, another vote for
The story or Plot (Quality of the writing and Dialog).
If you haven't got that in an adventure, regardless of sub-genre, you haven't really got anything, IMHO. Regardless of how pretty-looking, great-sounding, etc. a game might be, if there isn't an actual half-decent plot to not only draw me in but then keep me there, then I'm bound to lose interest. (Should add it doesn't have to be a huge amount of actual writing, per se, visible in the game.)
All of the above doesn't apply to non-adventure-type games at all though - I can spend hours blasting away at abstract shapes in something like Geometry Wars, just admiring the pretty, pretty colours...
So yes, in adventures, good writing is key for me, preferably in a strong, original voice. Everything else is icing on the hypothetical game-cake.
