I love traveling and so have done a fair amount of it. Because traveling is somewhat expensive, there is a certain cachet to describing yourself as a "world traveler" or "well traveled", but the definitions of these terms are vague.
I would say that how many places you have traveled to is relatively unimportant in gaining travel experience. What is much more important is how you have traveled. For instance, taking a package tour of Europe (or for that matter, Asia: package tours of China are quite popular among a certain set) means you might cover a lot of ground, yet you wouldn't really have experienced very much of the local culture or gained much traveling know-how since someone else was taking care of that for you. I consider myself a seasoned traveler (more or less, there is always more to learn).
To me, being well traveled means:
--you can leave for a several week trip to a foreign country without too much trouble (you know how to pack, what to bring, and how to get there), even at short notice;
--you can navigate any city (even in a foreign country) with relative confidence and ease, even if you don't speak the language, the day after your arrival;
--you are aware of some of the most common travel mistakes, and don't usually make them (always have a little cash; don't overpack; bring comfortable shoes, sunscreen and any medicines you will need; always know where your important documents are); and
--you don't expect foreign countries/places to be the same as your home, and you are prepared to be flexible with your expectations (People who aren't seasoned travelers very frequently make this error and then get grumpy.).
Usually having a lot of money works against being/becoming well traveled. For instance, experiencing a place as locals do means staying in (or at least spending time in) the non-fancy, non-central neighborhoods; and eating at cheap restaurants (almost no one can afford to eat out at nice places often when not on vacation); and taking public transportation (although in some places this might actually be privatized, like bush taxis in Africa). If you stay in a nice (almost always centrally located) hotel, eat out at high end restaurants, and take taxis (or private cars) everywhere, you will miss out on 90% of what a country is all about.
Being well traveled means that you have broadened your perspective and are aware that not everyone thinks/eats/believes/values the same things you do. It also (usually) makes people more tolerant, more understanding and more interesting. It is a great pity that Americans are by and large not at all a well traveled people. (And no, for the most part traveling within the US does not confer well traveled status, since the US has a remarkably homogeneous culture for such a large country.) I am lucky to live in Singapore, where international travel is so much easier.