Recordkeeping for taxes is tied to the statute of limitations, which is the period of time that a taxing authority technically has to audit you and ask you to produce those documents.
The basic statute for federal taxes is three years after the due date of the return (including extensions), or two years after a tax was paid, whichever is LATER. So, for example, if you are talking about 2012 returns, the statute expires on April 15, 2016 (or Oct 15 if you filed an extension for that year.) Some state statutes may be longer (My state, AZ, is four years.)
But note that a statute of limitations doesn't begin to run if you fail to file a return. So, if you didn't file a required 2000 return, the statute is still open for them to come after you, 13 years later!
Also, in some cases, the IRS has successfully claimed that a return that was filed was so incomeplete, leaving off a substantial part of reportable income, that it doesn't really count as "filed" at all, allowing the IRS to go after the person longer than 3 years.
There is also a longer statute applicable to payroll matters: If you are an employee, you need to keep records of employees hours and pay for at least seven years, or even longer if any of the employees are minors at the time. Check with your attorney or tax advisor.
WHAT records have to be kept this long? Certainly copies of returns, and all documentation used in its preparation (W-2, 1099s, mortgage statements, and accounting of deductions.) Actual receipts for business expenses aren't required, if the total on the receipt is under $75, but you need a written record of some sort, such as a check register or Quickbooks printout, showing the date, payee, amount, and what it was for.
My state (AZ) sometimes freaks out and asks for copies of returns back about 7 years. I tell them that the statute is only 4, and they respond that is only the case if a return is filed, and they say it wasn't, so the copy should have been kept indefinitely. It's a "chicken or the egg" type argument, so I usually suggest my clients keep at least copies of returns (not all docymentation) for ten years, although it isn't technically a required.