The resonant version (with series supply inductor) is properly called a Baxandall oscillator.
Thanks Tim. The current fed Baxandall converter is a nice simple topology and really has very little to do with the Royer converter as Tim pointed out. Most people just repeat what they read on the internet without looking into the history and development of push pull self oscillating converters.
A little history. One of the first applications of the Royer oscillator was a linear voltage to frequency converter, this cut and paste from Wikipedia.
Royer, G. H. (1955). "A switching transistor D-C to A-C converter having an output frequency proportional to the D-C input voltage". Transactions of the American Institute of Electrical Engineers, Part I: Communication and Electronics. 74 (3): 322. doi:10.1109/TCE.1955.6372293.. A 1955 paper by Royer on his circuit.
The Royer was a popular topology in DC to DC converters back in the 60's to convert 12V to a higher voltage for tube based mobile transceivers. PYE used it in their VHF/UHF mobile tranceivers back in the day.
One improvement on the Royer was the Jensen converter which moved the saturating transformer from the power stage to the transistor base drive stage, it offered better efficiency at the expense of an additional drive transformer. It still gives you propertional base drive current which optimises transistor switching times. See Swithed mode power supplies by Billings et al.
A similar topology to the Jensen converter was used quite a lot in early PC/XT power supplies but only to make it self starting. Contol loop didn't rely on saturation and used TL494 or similar driver.
Jim Williams wrote some excellent application notes on current fed resonant self oscillating converters used as CCFL power supplies. Rather than reinvent the wheel you could use a small CCFL converter to generate your HV output, just add rectifier diodes.