This thing is sort of resonant, I posted it a... few weeks? ago. Just ignore the fact that it has a regulator anyway.
http://seventransistorlabs.com/Images/HVPower1.pngIdeally, you'd have a cap tuning the primary, which is somewhat loosely coupled to the secondary, which is tuned as well. The secondary tuning consists of a parallel cap (which sets the unloaded resonant frequency) and a series cap to the load (which, plus the parallel cap, sets the frequency under short circuit conditions). Kinda-sorta the idea is to make a Tesla coil, but not with a gratuitous voltage ratio; the coupling is tighter than that, which makes it easier to transfer power in a given size.
As it turns out, my transformer didn't have a lot of leakage inductance, so I ended up with a sort of multivibrator with quasi-resonant switching edges, and some squigglies. I didn't end up using a series capacitor on the output for this reason. Maybe I still should. Since this is a high voltage example, the parallel capacitance arises from simple winding capacitance, so I don't have to add anything explicit across the secondary.
In a double tuned circuit like this, you can tweak the parameters (driving frequency, primary resonance, secondary resonance loaded and unloaded, and coupling) to get better regulation, possibly even negative resistance for some range (i.e., a heavier load pulls resonance closer to the operating frequency, delivering more power). It's not completely helpless, but there's a lot of stuff to tweak (and a lot of potential for drift, and line and load sensitivity).
You could also couple to an over-driven transformer core and do ferroresonant regulation: normally, the winding resonates to an excessively high voltage, causing saturation on the peaks; which reduces the effective inductance, raising the resonant frequency and regulating voltage.
Tim