According to Ubisoft, next-gen console versions of Assassin's Creed IV: Black Flag will require an internet connection for the game's single player campaign. The reasoning behind the decision is due to all the social features they are implementing for the game and the PS4 influencing this decision.
Creative Director Jean Guesdon stated:
They did not clarify if the requirement means an "Always On" connection is needed or if the single player is playable and/or impacted without it.
The PC, PS3, and Xbox 360 versions will not have these features while the Wii U might be affected depending if Ubisoft includes those social features for that version.