The other writeups here are excellent, and capture the traditional jiaozi very well. But beyond pork fillings, beyond the Spring Festival fun of making end-of-winter jiaozi with the whole family, a revolution occurred in the early part of this century in the way jiaozi are made in China, particularly in Beijing. Notice how all the other writeups refer to only one kind of filling? That's a hint.
I am actually going to be bold and predict that what we are seeing with jiaozi may be the thin edge of the wedge as far as Chinese food "going a little bit fusion" is concerned. This is not a bad thing! Far from it. I cannot think of a national cuisine (Thai, Indian, Vietnamese, Mexican, etc.) that has not benefited from the everyone wins wonders of a little fusion. The traditional cuisine gets more recognition, and the traditional flavours and textures get used by smart chefs to make wonderful new things to eat.
So what's happened to the jiaozi? Essentially, it's been taken back to basics and reinvented. What did we always love about jiaozi? The skin, the steam magic, and the dipping sauce. What were we always a bit ambivalent towards? The filling. Usually a little stodgy and flavourless, as hinted in some of the other writeups here, the filling, when it was good, was just ok. Pork-plus was pretty much it.
And that's what's changed. Starting with "That jiaozi restaurant out near the Third Hospital (in Beijing), you know, that one started by the famous singer" the fillings have undergone quite a change recently. In case you think I am being silly with the name, that's what you'll actually have to say in a Beijing taxi to get to the place. The singer was famous in a very, well, one hit wonder kind of way. But the fillings are fabulous. Never missing a beat, other jiaozi restaurants in Haidian have almost all taken up the new style, and it's now spread widely in Northern China.
So what's in these new fillings? Everything. You can order as if you're at a regular Chinese restaurant, whatever dish you can think up, and they put it in a wonderful little steamed dumpling for you! Xihongshi chao jidan? (Tomato'n'eggs.) Done. Gan bian bian dou? (Spicy dry fried green beans.) Done. Fish? Sure, done. Chicken with your favourite vegetable? No problem, how many do you want?
And that brings me to the final change that's come about. One of the historical problems with ordering jiaozi is that you had to order so many of the same kind before the cook would make them for you, because the filling was "jiaozi only" so minimum numbers were high, sometimes half a pound of one flavour! Now, because everything on the menu is essentially open to popping into a jiaozi, and mostly it tastes better that way, the minimum order number has come way, way down. Most places these days you can get away with ordering just ten jiaozi of one flavour, and that is great news for small parties or eating on your own.
In summary, if you haven't had jiaozi, in Beijing, since 2001, you haven't had jiaozi!