There are some really, really good answers above. That will not stop me from sharing though... ;-)
1- DO NOT AUTOMATICALLY TRUST AN "Electrician" FOR DATA CABLE
There are things that electricians 'have always done' that are bad juju for data cable. Pulling hard to get cable through holes, running too close/parallel to high voltage AC, tight bends and too-tight stapling can all degrade or destroy the data carrying capability of your new wires. Some may know what they are doing, but it's not guaranteed.
2- Run all your cables back to a common interconnection point. Bonus points if this is in an unfinished portion of the house so that end of future port expansion is easier. Put a dedicated power circuit there and plan on putting in a decent UPS to keep your network up through power blips and outages.
2- If it's worth pulling one wire to a drop, it's worth pulling two (or more) .. think... smart TV, xbox, and a player of some sort - that's three connections that may not always be desired in the same side of a room.
3- Put at least two drops in each room - preferably on opposite walls. Personally, I'd put a 4-port drop on each wall, but I'm a tech guy, so YMMV.
4- Plan on proper wifi access points. (and disable whatever comes pre-activated inside your internet box) Ceilings are the best spots, but each house is different.
5- Use the best cable and terminations you can get. Not that long ago a 10mb network on slightly upgraded phone wire was state of the art. If you put in Cat 6, use the right terminations, and your wiring guy knows his shit, you are good for at least gigabit ethernet, if not 10g.
6- Plan on POE capability. It makes installation of access points, security cameras, environmental sensors, etc much simpler.
7- If you can, have your in-wall data run through good sized flexible conduit. If will make adding other wire later on
much, much easier... possible. Who knows when you might need a different kind of wire or fiber or...??
8- LABEL THE DROPS/PORTS ON EACH END
9- Get a NAS box that will work as a DVR for IP security cameras. Don't cheap out - get something decent. I recommend putting this near the service area where your UPS and switch will be. As a bonus, in addition to security footage, it can serve as a family data backup location.