To me, a Classical education is a humanities based one where traditional subjects are taught based on traditional concepts of child development. That's my definition in a nutshell!
I guess I'm something of a traditionalist
(educationally, at least!)
My larger definition would also include the three stages of development: grammar, when you're just learning the rules; logic, when you have the rules down and are learning how to critically think about the subjects you're studying; and rhetoric, where you're now ready to really run with what you're studying. It would also talk about each of the three four year stages cover more or less the same materials, at different levels, and so by the time the student is ready to study a subject in depth, he's already covered that subject twice before. So while obviously some review will be needed, you won't have to start from scratch. It's very systematic, with the subjects fairly carefully divided. It also tries to be cohesive within each year: so in 2nd, 6th, and 10th grade you study the Medieval and Renaissance period. Not just the history, but you also read fiction books about the period, study the art and music, and for science in those three years you study Chemistry.
One of the things that I PARTICULARLY like about this curriculum is that you study the entire world, not just "European History." Studying separate regions separately is all fine and good for prehistory, but as soon as there is contact, things get complicated. It wasn't until I was really in college before I understood how the history of different regions really matched up, and the connections different regions had with eachother.
Now, as to "traditional" it is kind of a weird word, isn't it? First off, I don't consider the way that public schools teach things to be "traditional." They jump around far too much, and leave out far too many knowledge gaps. For example, in most elementary school classrooms, science or history is something that the teacher kind of gets to when they get to it, and it usually hops around all over the place (history is usually based on holidays). It isn't until middle school that students usually have a separate science class that is divided up by field (biology in 7th grade, etc). And by that time, knowledge is so haphazard and the kids who were in Mrs. Smith's 5th grade class made volcanos but never studied weather, while the kids in Mr. Jones's 5th grade class spent all year learning the different types of clouds but wouldn't be able to identify the parts of a plant to save their lives. William J. Bennett writes a lot about this in his books, in particular there's a pamphlet called James Madison High School where he outlines his ideal curriculum and talks specifically about this problem.
So in this case, "traditional" is used to mean old-fashioned, way back to a time that never actually existed, but I think it makes some of us feel better to feel that we're just returning to our educational roots
Way back in the yonder days of yore when we walked 10 miles uphill both ways in the snow to school... and also got a broad, systematic overview of many subjects, instead of just random unit studies done at the teacher's whim. A book that I found really solidified my views on what's wrong with the way that public schools present subjects is "The Schools We Need," by E.D. Hirsch.
As for the traditional view of child development, it's my own personal hill to die on that I think people except children to grow up far too fast, mentally. Teachers and parents expect young children to think like adults, and they just don't. Kids are smart, however, and they learn to regurgitate things that they don't really understand in a way that makes the adults around them think that they learned them. This is why I really like the trivium: the first 4 years are just a year of absorption and regurgitation, and you don't ask the child to analyze the materials in depth or draw broad conclusions. You just ask them to learn all the things that kids love to learn: stories, games, how people lived, what people did, why the magnetized needle points north, what countries are where, what's a conifer and how can you tell it apart from say an oak tree. Kids love to make connections, and some are spurious, but you just kind of roll with it. (The grow up too fast thing is what drew me to Waldorf for a while, but I also believe that kids love science and love to know how things work, and it's a total deal-breaker that in Waldorf you're not supposed to tell kids the truth about anything science-y until they're quite old.)
As you can see from my sig, my children are young and I'm prepared to be flexible based on their needs. However, I've spent a good portion of my life teaching and watching kids, and drawn some overall conclusions that make the Classical model to be my personal ideal way to educate a child. I absolutely understand the appeal of some other curricula, but the Well Trained Mind sold me, and then various other readings I've done on child development and educational theories really cemented my dedication. I don't love every aspect of it: I have no interest in pared down classics for kids, with a few exceptions (there ARE some excellent retellings of various ancient sagas). And the actual Story of the World stuff that you're supposed to read is 1) super dry and 2) too religious for me (though it claims to be secular, it also presents Bible stories as being real history).
The WTM is the ultimate guide to a Classical education, but its popularity has spurned many other variations (just like, as you mention, various different Waldorf curricula offer various different perspectives). As the PP said, if you're interested in the Classical model, the WTM has a wonderful and very active discussion board.
(Eep: sorry for the novel-length reply! Obviously, this is just subject that interests me, and it comes up fairly rarely on this board so I love to expound on it!)
, History Pockets, and most of the additional readings that HO suggests. We also have SotW (on CD, too, which for us is much more enjoyable), which HO suggests to use as a spine, but we don't really use it that way. 
