It varies heavily from person to person. What some people may find valuable, others may find obnoxious.
What is a game for, even?
Some aim to tell a story (RPGs and a lot of MMS games), some are just trying to give the player a good time (Mario, X-COM), others are to show off fancy new technologies the industry may be able to put to good use (Shattered Horizon, recent Battlefield games).
Ultimately they should be fun, or failing that, interesting and thought provoking. Though as I said, what is "fun" or "interesting" depends on the person.
