Publically, the IRS says you should keep your financial records for 3 years because they can audit you for up to 3 years after the time. However, they are allowed to go back as far as 7 years, so I recommend keeping your records for 7 years.
There are several reasons you may want to keep your financial records. One reason is if you wanted/needed to sue someone later on about a product or other financial reason, you would want to have the record that shows how much you paid. Another reason is if a bank or someone had an error with your finances, you would want the evidence that shows how much you should have.