You are not legally required to keep your returns.
However, in most cases, the IRS has three years to examine your federal tax return, so you should keep your federal tax records along with any supporting documentation (receipts, appraisals, etc.) for at least that long. Four years is even better.
See also the IRS's How long should I keep records? for exceptions to the general rules.
Many states follow the IRS's lead, but not all (for example, California can audit back four years). To be safe, we recommend visiting your state's website or contacting them for specifics.
See How long do I need keep my tax return paperwork?