Occasionally I gather old bills, receipts, checks, ATM slips, etc., to stuff them into a trash bag. How long should I keep such things? And I’ve read that a shredder that only cuts papers into long strips isn’t adequate, when a patient crook can (supposedly) paste them back together…
I use the Fellowes P400C-2 http://www.fellowes.com/category.aspx?catalog=Fellowes+Web+Site+Catalog&category=Personal%3A+%40+Home(Fellowes+Web+Site+Catalog)&main=0&sub=4&path=Business+Machines(Fellowes+Web+Site+Catalog)|||Paper+Shredders+%26+Supplies(Fellowes+Web+Site+Catalog)|||Shredders(Fellowes+Web+Site+Catalog)|||Personal%3A+%40+Home(Fellowes+Web+Site+Catalog)&sep=y#32700 (third from the bottom).
The crook must be of the ultra-patient, anal-retentive kind to reassemble the shredded documents 
I went to that website, but all I could raise was the frame–no product pictures.
I’ve given serious thought to mixing the shredded pieces in a bucket with water and plaster–to turn the documents into a useless mass of papier-mache.
Dougie, nobody is going to dig through your trash, pull out heaps of little tiny strips of paper and then spend hours reassembling them to get the last 4 digits of your Visa card number and the location of your favorite gas station.
If you have info that is really worth that much effort to recover, the gang of master thieves probably already has a tracer implanted in your skin, blueprints of your house and master keys for all the locks.
Assuming that you are moderately paranoid like me, get yourself a $50 crosscut shredder, drop your secret stuff in there and shake the waste basket to mix up the random bits of confetti, you’re safe. Toss the bits into the recycle bin or use 'em to light the fireplace or pack gifts in 'em or whatever you want.
IIRC the IRS asks you to keep tax returns for the last three years. I keep receipts for big purchases at least until the warranty has expired, most other credit card receipts I shred after I’ve used the item and paid that bill.
When I get a rush of paranoia, I just wait to throw the stuff out til I have some really nasty trash - kitty litter, biohazard, extremely old broccoli…
But I imagine any would-be identity thief would rapidly bump into my screaming avalanche of student debt and decide s/he would much rather be someone else 
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I burn them in my backyard fire-pit thingy.
Well, that may be easy for you to say in Wisconsin; but in Southern California we used to have back-yard incinerators until they were prohibited in 1957.
(One year my Mom hid the Halloween candy too well in the middle of October. Then she dumped the trash into the incinerator, dropped a lighted match in and–a moment too late she remembered where she had hidden the candy! )