Did you see the Jodie Foster film "Panic Room"? I didn't, but I know the basic premise: a woman and her child are trapped in a room designed to keep out everybody and anybody. The problem is that the room also contains millions of dollars. You probably don't have millions of dollars to protect, but the idea of a safe room is a pretty appealing one. It doesn't necessarily have to be a room to protect you from intruders. Maybe you live in an area of the country that gets a lot of tornadoes or you're worried about a zombie apocalypse.
So what makes a safe room safe? FEMA has guidelines on building a residential safe room, so check those out. Normally it's on a ground floor or even below ground, with a solid foundation. A strong door, preferably made of steel, needs to be resistant to battering, bullets, and fire. If the rest of your house is built with wooden studs, the safe room should have steel studs (because they're fire-resistant) and a reinforced ceiling to prevent intruders from entering and debris from coming through. You can also build the walls out of concrete, or include things like metal mesh. Now that you have your cage built, so to speak, what else can you do to make it safe? If you really want to go all out, you can install a separate ventilation system, power supply and telephone line. That way if anything happens to those things in the main house, you'll be just fine in the safe room.
If telephone lines are totally down, though, consider a satellite phone or ham radio for communication. And since you may be in there for awhile, you'll need cots, clothing, first aid supplies, ready-to-eat food, water, a portable toilet, flashlights and any other gear you might deem necessary for the long haul.