After 6-12 months. Parents should put babies down to sleep on their backs, not on their tummies. Younger babies can't roll over yet, so they tend to stay on their backs (which is good, since the younger babies have a higher chance of sids). Older babies are able to roll back and forth, and they are also less likely to die of sids. So, parents don't have to get up at night just to check their babies' positions.
When they can roll. When babies can roll over, and do it well from front to back, it is safe for them to sleep on their bellies because they can push themselves over if they need. Of course, when they can roll from front to back and they go to their bellies on their own, it is beyond your control!