I just bought a shredder yesterday, and then I came across “The Torn-Up Credit Card Application” which shows that you should buy one as well.
From LifeHacker (who pointed me to this experiment):
[snip]
…it turns out that simply tearing apart the forms may not be enough of a deterrent.
Results of the Torn-Up Credit Card Application experiment show that a bank may issue a credit card when the application is received on a taped-together form, so shredding such documents is a much better approach.
[snip]
I got mine at Target, which probably means that I paid too much for it. I like it, though I haven’t used it for a lot yet.
I’ll report back when I start to do a lot of shredding.