You should keep the supporting documents for 7 years.
As for the returns, I always recommend keeping them, in a secure place, forever, along with any Form W-2s. Tax returns are a sort of “diary” for a person’s life.
For example, let’s say that someone has a need to provide a complete and accurate employment history (perhaps to apply for a government job or get a security clearance). The person might not remember when past jobs began or ended, but the old tax returns are an excellent record.
As another example, one of my clients recently had a complex property transaction, and we needed information from several years during the 1970s. The data would have been easily obtained from her tax returns. She hadn’t kept the returns, however, so we went through hell (read: high fees for me) recreating the history.