I make 3 piles:
stuff I wanna look at (comics, parade, and coupons)
rest of the actual newspaper material (I give to a coworker for her puppies)
glossy paper sale ads (garbage)

I always look at the coupons first, then set aside the booklet for another coworker. Then I glance through Parade. Comics are set aside for whenever I get a chance to read them.