jp brings up a good point. The short answer is, keep the receipts for at least three years after you file or after any amendments you make.
But everyone should check their Social Security statement at least every couple of years. It will show a gap in your earnings history for any year where they think you didn't file a return and pay SE tax (if self-employed) or where no W-2 was filed (if an employee). The first time I got one of those, there was a gap for 1987, which was the last year I worked for a company that filed chapter 11 bankruptcy three weeks after the end of the year. Apparently they never reported my W-2. Luckily (because I'm a pack rat) I still had all my tax documents from that year (this was about 10 years later that I discovered this) and was able to send SS the W-2 for that year and get credit for my earnings and SS payments.
So this is one way to spot if you either failed to file a return or it somehow got lost between your mailbox and the IRS computer.
So I would say, keep your receipts for at least three years after you file or you have confirmed that the return was received *and processed* (don't rely on those postal receipts or delivery confirmation), whichever comes later.
You can get your SS statement on the ssa.gov website or they should mail you one about two months before your birthday each year (they used to do this, then stopped, and are now doing it again).
Unfortunately, while there is a statute of limitations for auditing a return (three years) and a statute of limitations for collecting tax once it has been assessed (ten years) there is no statute of limitations for demanding you file a return and pay tax and all those years of penalties and interest in the event a return was required but was never filed.
I have filed tax returns going back as much as ten to thirteen years for more than one client.
Time to build a bigger bridge.