Here are some thoughts I had and have questions on:

1. Do I need to run Cat 5 wiring or the latest thing to each bedroom and connect them to the office where the router will be?

It's easier (and cheaper) to take care of this while building, so I would do it. Hardwired is not a bad thing in a house.

2. I was thinking about putting a speaker in some rooms with them all connected to the office. I think this would be cool to listen to music throughout the house. Is this crazy?

You might consider it for a communications system too. Instead of yelling through the house, pick up the mic and broadcast over your house intercom.

3. I have a family room in the basement that will sort of be the theater room. What type of surround sound should I get and how do I wire it?

I'll defer to others more knowledgeable on this.

4. Should I have Dish or Directv pre-wire my house or will the electrician do that?

I would imagine an electrician can do this.

Any other cool things I should be aware of? I probably should run internet access to where I want my TVs right? With online streaming a reality in the future, I should do this. Is Cat 5 the best?

If you live in an area where you get snow, put in a heated driveway.