Sony has announced that the PS4 will require you to have a PlayStation Plus subscription to play multiplayer.
This is similar to what Microsoft already does with its Xbox LIVE Gold membership. Still PS4 owners will have the chance to enjoy offline game modes freely without any hassles. The PS4 does not require you to connect the device online or anything like that.
Existing PlayStation Plus memberships will carry over to the PS4. In the USA, a PS Plus subscription is less than $5 per month.