We systematically study the X-ray and ultraviolet emission of a subsample of M dwarfs from a recent proper-motion survey, selecting all M dwarfs within 10pc to obtain a nearly volume-limited sample (~90% completeness). Archival ROSAT, XMM-Newton and GALEX data are combined with published spectroscopic studies of Halpha emission and rotation to obtain a broad picture of stellar activity on M dwarfs. We make use of synthetic model spectra to determine the relative contributions of photospheric and chromospheric emission to the ultraviolet flux. We also analyse the same diagnostics for a comparison sample of young M dwarfs in the TWHya association (~10Myrs). We find that generally the emission in the GALEX bands is dominated by the chromosphere but the photospheric component is not negligible in early-M field dwarfs. The surface fluxes for the Halpha, near-ultraviolet, far-ultraviolet and X-ray emission are connected via a power law dependence. We present here for the first time such flux-flux relations involving broad-band ultraviolet emission for M dwarfs. For given spectral type the activity indices, defined as flux ratio between the activity diagnostic and the bolometric flux of the star, display a spread of 2-3 dex which is largest for M4 stars. The mean activity index for fast rotators, likely representing the saturation level, decreases from X-rays over the FUV to the NUV band and Halpha, i.e. the fractional radiation output increases with atmospheric height. The comparison to the ultraviolet and X-ray properties of TWHya members shows a drop of nearly three orders of magnitude for the luminosity in these bands between ~10Myr and few Gyrs age. A few young field dwarfs (< 1Gyr) in the 10pc sample bridge the gap indicating that the drop in magnetic activity with age is a continuous process. The slope of the age decay is steeper for the X-ray than for the UV luminosity.
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