Legal Lad and Get-it-Done Guy tell you what paperwork you need to keep and how long.
Military and Selective Service Records: Keep safe all your military records for future benefits and future service. The military will likely keep a copy, but if you ever get into a dispute with the military over your records, it is very important to have your own copy.
Immigration Documents: Immigration documents are extremely important for the rest of your life for purposes of immigrating again, and to prove eligibility to vote in some circumstances.
GDG: There are many records you want to keep temporarily, but then get rid of, like Pat's phone number. You remember Pat? The one who dumped you in 8th grade? Yes, it's finally time to move on. Basically, you can toss documents that don’t matter anymore. Any time you pay money, keep a receipt to prove you paid. Do this for bills, credit card purchases, mortgage payments, or installment payments. Keep it until you get the next statement showing your payment and the new balance. Then you can toss the receipt, and just keep the current statement. Once you get a new statement, you can shred the current one and keep the new one. On rare occasions, I've needed to find a statement that was months or years old, but generally for a small fee, my bank or mortgage company has been able to provide a copy, easily.
When you pay off a loan, keep a copy of the final statement proving you paid it. That way, if your credit record ever gets screwed up or someone forwards your closed loan to a collection agency, you can clear up the matter quickly. I keep loan payoff proof for seven years because I like the number seven.
When you're owed money, keep proof! If you send someone a bill or an invoice, keep a copy until it's paid. If you are awarded money as a rebate, or from a dispute award, or because you loaned someone money, get it in writing so you can prove the money should be yours. If you're loaning money to friends or family, consider using VirginMoneyUS.com. They help people loan money and track the loans in a professional manner.