When I was first married, Robert told me to use his shredder to shred anything with any kind of personal information on it. I regularly fill up and dispose of several bags of shredded paper each year.
I have recently been wondering should I bother with shredding the address labels from magazines and other pieces of advertising that I get. I did a search and came up with these helpful articles:
Learn What to Shred
Secure Paper Shredding to Prevent Identity Theft
How to Shred Documents and Stop Identity Theft
8 Things You Should Shred Right Now
One surprising thing I learned is that it is perfectly legal for people to dig through your garbage. The short answer to my question is this: If in doubt, shred it!
One tip to help with cleanup is to keep an appropriately-sized trash bag in the shredder can. You can keep empty trashbags under the one being used so that you always have another one hand to replace the one being disposed.
Another tip is to go to DMAchoice.org to remove yourself from mailing lists.