The PS4 will not be able to play PS3 game. The PS4 will not be using the Cell processor (to save costs of course) so backwards compatibility will be a no go for next gen.

Emulation may be possible in the future, but Sony seems to have found a stop gap with Gaikai (the streaming service they bought for $380 million last year). I would imagine PS+ integration or some kind of detection system where you put you PS3 game in, it registers it with your account and lets you stream it (sky's the limit before the reveal right?).

What would be really neat is if we could get Gaikai on the Vita and PC's!