According to Shuhei Yoshida, president of Sony Worldwide Studios, the next-gen PlayStation won't support the PS3's Dual Shock controller. However, the original Move motion controller will be a part of Sony's next-gen plan
Yoshida said, "No, [PS4] doesn't support DualShock 3, but it does support PS Move."
This isn't surprising news, given that the new Dual Shock controller features a touchpad that presumably offers new controller input mechanics for games that wouldn't be possible with the previous iteration of the controller. Move support was also expected, as the new Dual Shock actually features a move sensor built into the controller. However, it does mean that, if you want to play multiplayer amongst friends on the couch, you'll have to pony up the money for all-new controllers.
Source: IGN