Be warned, this write-up contains some mild spoilers for most Miyazaki
I want to adress some of the trends we find in these movies that I've noticed while watching them and while watching the masterpiece AMV "Memories Dance" By Vlad J. Pohnert (see www.animemusicvideos.org).
First of all, there is almost always a strong lead female role. In Laputa: Castle in the Sky we had the leader of the pirates, Ma Dola. In Nausicaa of the Valley of Wind, we can cite the general of the invading army. In Mononoke Hime (Princess Mononoke) there is Lady Iboshi.
There is usually a young female lead with male supporting role of the same age, and occasionally vice-versa. Typically, the movie ends with the two falling in love to one degreee or another: sometimes it's made obvious, others, it's implied.
Animals of one kind or another are almost always present. My Neighbor Totoro is pretty obvious about this, we also have giant insects, animal gods, pets and, if we stretch the imagination a little, robots which behave in a similar manner to animals (I'm thinking Laputa in this case).
Hayao Miyazaki seems to be obsessed with flying. Some of his movies are entirely centered around it; both Laputa and Nausicaa incorporate massive flying vehicles of one kind or another. The ending of On Your Mark has the freed angel flying off into the sky. Kiki's Delivery Service has both the witch broom and the man-powered glider of Kiki's friend.
Also, perhaps less obvious, is that there is rarely a distinction between black and white good vs. evil. This can be said of most anime, but it is especially visible in these movies and often becomes one of the major themes. Even the people cast as the "villains" usually have a genuinely good reason for doing what they're doing and don't perceive themselves as being evil. The only movie I can see as detracting from this is Laputa.
Finally, something a little more trivial but interesting all the same: the young lead females always seem to have the same hairstyle. Again, the only exception is Laputa, but the movie compensates in the end by having the girl's braids shot off.