How many years after an account has been closed (i.e. checking, credit card, brokerage accounts, not accounts like utilities, auto/home insurance, etc.) are you comfortable throwing out (trash, not recycling) the statements vs. shredding them? "Comfortable" here is with respect to identity theft worries, not taxing authority worries.
Finally time to attack some of the attic clutter and among other things are statements going back to 1987. So the stack of potential shreddables will be very tall. (I of course will be keeping all tax returns and will be keeping supporting documentation for the past six years' returns).
(Though I suppose the best thing is to probably just play it safe and bring everything to a reputable bulk shredder. Too bad my town doesn't allow outside burning, though...)