The PlayStation 4 will not be backwards compatible.
Got a bunch of PS3, PS2, or PS1 games? Too bad, bucko! You won't be able to play them on the PS4 when it launches this fall. Oh, you can probably jam those disks into the console but that's about as far as you're going to get. Heck, all those PSN titles you bought? Nope, not going to be able to play those either.
How does that make you feel?