If you're concerned about identity theft, then you may want to consider a shredder for disposing of papers like credit card bills or applications. The Frugal for Life blog advises against the older strip cutter type of shredder:
"In my search I have found that cross-cutter paper shredders are better than the the strip cutters, that have been around longer. Strip cutter shredders still allow the criminal to reassemble the document so that it can be used. Where as cross cutters make the process MUCH more difficult if not impossible."
While many businesses use shredding services for sensitive documents, most people aren't as careful at home. The Consumerist blog says "committed identity thieves can piece together strip-shredded documents, and credit card companies readily accept torn applications."
The also offer a few ways you can make use of the shredded paper - packing material, pet beds or ... homebrew confetti.
Buy a Shredder [Frugal for Life]