Hydraulic systems have a 'primary' pump and at least one 'backup' pump - the backup pumps are generally electric or air driven pumps (sometimes both). In the case of the 777, the primary pump source for the left and right is the engine driven pumps (EDP) while the center uses an electric pump.
As wiggy notes, the APU can't drive the EDPs directly but can and does provide the electric and/or pneumatic source for the other hydraulic pumps.
JeroenD, unlike the 747, the 777 APU is in-flight operable throughout the flight envelope (although it can't be used as a pneumatic source above some altitude). You are correct, the 747-400 (and earlier models) don't need a RAT, the windmilling engines will provide adequate hydraulics for basic aircraft control in an all-engine out condition. However the 747-8/8F does need a RAT - the combination of higher bypass engines (lower windmilling speeds) and higher hydraulic loads due to the new wing made the RAT mandatory.