As you know DMs do most of the job for the campaign (maps, plot, NPCs etc) and quite a bit of storytelling. Players, on the other side, bring in their creativity and add extra spice to the game sessions, plus they steer the overall story direction.
What would you recommend as a way to make the players do 'more'? What could they devise, of the universe the DM has in mind, so that it does not give them too big of a help in the future but, at the same time, it reduces the DM's burden without scrambling his/her plans?
I know that not all players like to invest their off-session time in RPG thinking, but, luckily, some do.
I've browsed the site and could find only one vaguely similar topic: How do you compensate your game master?, but i'm talking more of things to do for the campaign, not extra (like pizza). Please point me to more of those topics in case i've missed them!
EDIT: the game I generally play is DnD 3.5. I'm a bit challenged by describing the fashion... I think of it in terms of a great adventure with a party that roams the world, takes part in a major plot but also gets to say its own about in (sort of like the hobbits in LOTR, they are carried in the adventure at first, then they shape a part of it)