As part of Sony's PS4 announcement conference today, the company detailed how on-demand game streaming will work with the new console. That technology is also informing how backward compatibilty will function on the PS4.
The bad news is that PS3 games will not be natively supported on the PS4. However, through the magic of Gaikai, Sony is working on getting every PlayStation game--be it PSOne, PlayStation 2, or PlayStation 3--to be playable on the PlayStation 4.
Don't look for that functionality day one, however. Perry said that while the cloud streaming of legacy PlayStation games has been greenlit, the functionality is to be rolled out in phases.