I would double up rooms for each circuit. So four rooms = 2 circuits. At the location of the entertainment center, I would provide at least one dedicated circuit, and a circuit for the bathroom. Put in at least two lighting circuits, so that you aren't left completely in the dark if somehow you trip a breaker. Use fan rated boxes for your regular lights and provide bracing. Run 14-3 (or 12-3) to them from the switch box, which I would make double gang even if not installing a fan just yet. Little things like this don't cost that much now, and save a whole lot of work if you want to add something in the future.
Also, conduit is cheap, so you might want to run maybe two 1" conduits to the location of your entertainment center from some accessible portion of the basement. Overhead projectors are popular, so maybe a receptacle in the ceiling along with an empty pipe to the entertainment center. Now is a good time to wire for future audio. Contrary to what audiophiles say, there is no need to by the super-expensive cables for this
You could even put the boxes in, and run blue smurf tubing to them, so that you are covered for any future technological upgrades. Don't forget the smoke and CO alarms.