There are also rules about how long wires have to be before you have to step up to the next higher (eg, smaller numbered) gauge. You probably won't run into those limitations. Also, you can't hide connections between wires in an inaccessible space, although it's doubtful that you'll do that anyway. I would do as Josh says and get a book on wiring. It's relatively simple. Also, be aware that a select few areas of the country won't let you do your own wiring (while other areas don't have an inspection system). Ideally, you should apply for a permit and have your work inspected if your area requires such inspections. Another possible limitation is how many breakers you already have. I'd have to check my book (the national electrical code, NEC), but I believe there's a limit to how much "over" the panel you can go. In other words, if you have a 200 amp panel and have 200 amps of breakers, then you add three dedicated 20 amp breakers, would you be over the limit (even assuming you don't really use 60 amps)? Let me know if that's the situation, and I'll look it up for you.
One caveat is that most breaker boxes have the grounds and neutrals connected to the same location in the box. However, some areas of the country are moving to separate grounds and neutrals that are then connected together at one location. Take the cover off your breaker box and it'll be easy to find out what type you have. Also, the wires have to be supported every 4 feet or so, but any book you buy should explain that.