The IRS generally requires you to keep certain things for 3 years (4 years for payroll).  However, in some cases the starting date of the three years is funky, so I recommend keeping them for 4 years.

Some tax organizations may recommend longer (such as 7 years), but that isn't required by the IRS.

With that being said, I tend to keep some records of current clients for longer, in case I need to refer to them or in case my current client somehow ends up in an audit further than three years back.