To me, touring is traveling on a bike. That is, going out with a sense of adventure to go somewhere, rather than training, racing, riding to work. All of my touring has been supported, that is with someone else carrying most of my gear. However, I have taken many weeklong supported trips that were relatively inexpensive (less than $500). Others don't consider it touring unless go unsupported -- you carry all of your gear. I think this definition is too limiting because not everyone wants to invest the money in loaded touring. You can take some great trips on supported tours for very reasonable prices, and do it on just about any road-worthy bicycle in good mechanical condition.
I am just starting to acquire the gear needed to do some unsupported touring, but it is expensive. You need sturdier wheels, larger tires, different gearing, racks, panniers, possibly camping gear. It adds up to a lot of money and takes a while to compile unless you've got the money to begin with. Hopefully I will try my first unsupported tour this spring. If I don't like it, I will continue to do supported tours and have no regrets.