We report VLA radio observations of 29 SNe with ages ranging from 10 days to about 90 years past explosion. Included are detections of known radio SNe 1950B, 1957D, 1970G, 1983N, the suspected radio SN 1923A, and the possible radio SN 1961V. None of the remaining 23 observations resulted in detections, implying that most SNe are not detectable radio emitters. To investigate this, we have used Chevalier's "standard model" to derive (upper limits to) the mass-loss rates for the supernova progenitors. The various assumptions used in the calculations are discussed. These upper limits to the fluxes are consistent with a lack of circumstellar material needed to provide detectable radio emission. Examination of the radio luminosities of our supernovae as a function of age past explosion indicates that the SNe II upper limits are more consistent with the extrapolated light curves of SN 1980K than of SN 1979C, suggesting that SN 1980K might be a more typical radio emitter than SN 1979C. Finally, we present results of analyses of the non-SN radio sources in our maps and make tentative identifications of these sources where possible.