We report photometry of the helium-rich cataclysmic variable ES Ceti during 2001-2004. The star is roughly stable at V ~ 17.0 and has a light curve dominated by a single period of 620 s, which remains measurably constant over the 3 year baseline. The weight of evidence suggests that this is the true orbital period of the underlying binary, not a "superhump" as initially assumed. We report GALEX ultraviolet magnitudes, which establish a very blue flux distribution (F_nu ~ nu^1.3), and therefore a large bolometric correction. Other evidence (the very strong He II 4686 emission, and a ROSAT detection in soft X-rays) also indicates a strong EUV source, and comparison to helium-atmosphere models suggests a temperature of 130+-10 kK. For a distance of 350 pc, we estimate a luminosity of (0.8-1.7)x10^34 erg/s, yielding a mass accretion rate of (2-4)x10^-9 M_sol/yr onto an assumed 0.7 M_sol white dwarf. This appears to be about as expected for white dwarfs orbiting each other in a 10 minute binary, assuming that mass transfer is powered by gravitational radiation losses. We estimate mean accretion rates for other helium-rich cataclysmic variables, and find that they also follow the expected M-dot ~ P_o^-5 relation. There is some evidence (the lack of superhumps, and the small apparent size of the luminous region) that the mass transfer stream in ES Cet directly strikes the white dwarf, rather than circularizing to form an accretion disk. Comment: PDF, 26 pages, 3 tables, 9 figures; accepted, in press, to appear February 2005, PASP; more info at http://cba.phys.columbia.edu/