Using a paper shredder is very important. Make sure you shred any papers (excluding tax, financial, and medical documents) that have your name, address, birthdate, or social security number. Make sure your shredder is a "cross-cut" shredder. This makes your shredded documents shred into even tinier pieces.
Apparently just ripping up credit card applications is not good enough - as evidence by this story of a man who taped back together his torn credit card application and was still able to get a credit card!