[Abridged] As part of our on-going investigation into the magnetic field properties of ultracool dwarfs, we present simultaneous radio, X-ray, and H-alpha observations of three M9.5-L2.5 dwarfs (BRI0021-0214, LSR060230.4+391059, and 2MASSJ052338.2-140302). We do not detect X-ray or radio emission from any of the three sources, despite previous detections of radio emission from BRI0021 and 2M0523-14. Steady and variable H-alpha emission are detected from 2M0523-14 and BRI0021, respectively, while no H-alpha emission is detected from LSR0602+39. Overall, our survey of nine M8-L5 dwarfs doubles the number of ultracool dwarfs observed in X-rays, and triples the number of L dwarfs, providing in addition the deepest limits to date, log(L_X/L_bol)<-5. With this larger sample we find the first clear evidence for a substantial reduction in X-ray activity, by about two orders of magnitude, from mid-M to mid-L dwarfs. We find that the decline in both X-rays and H-alpha roughly follows L_{X,Halpha}/L_bol ~ 10^[-0.4x(SP-M6)] for SP>M6. In the radio band, however, the luminosity remains relatively unchanged from M0 to L4, leading to a substantial increase in L_rad/L_bol. Our survey also provides the first comprehensive set of simultaneous radio/X-ray/H-alpha observations of ultracool dwarfs, and reveals a clear breakdown of the radio/X-ray correlation beyond spectral type M7, evolving smoothly from L_{ u,rad}/L_X ~ 10^-15.5 to ~10^-11.5 Hz^-1 over the narrow spectral type range M7-M9. This breakdown reflects the substantial reduction in X-ray activity beyond M7, but its physical origin remains unclear since, as evidenced by the uniform radio emission, there is no drop in the field dissipation and particle acceleration efficiency.
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