I second what Dave said. Nobody in history has ever said, "Darn, I ran too many wires..." I have Cat5e and RG6QS all over my theater and game room. Most of it never gets used, but it's good that it's there, just in case.
For power, I have a 20A circuit just for my pins (I can only fit 5 in my space, max). Lights have their own circuit. Theater equipment closet has its own circuit. And the rest of the outlets in the theater have their own circuit. Overkill, for sure, but again, why not?
Regarding low-voltage stuff, if you're building new, instead of running wires to places you don't need yet, you might want to consider installing conduit. That way in the future, you can simply pull whatever wires you want through that. I have a conduit in the theater going from the projector to the equipment closet, and another one from the equipment closet to the central area in the house. The builder also installed conduit from the central area to the attic - which is great, if I ever want to run any cables to literally any room on the second floor. I haven't used it, but I'm glad it's there, and conduit is even cheaper than cable to install.