We present and discuss the radio observations of 27 Type Ia supernovae (SNe Ia), observed over two decades with the Very Large Array. No SN Ia has been detected so far in the radio, implying a very low density for any possible circumstellar material established by the progenitor, or progenitor system, before explosion. We derive 2 s upper limits to a steady mass-loss rate for individual SN systems as low as 63 x 10 super(-8) M sub(z) yr super(-1), which argues strongly against white dwarf accretion via a stellar wind from a massive binary companion in the symbiotic star, an example of the "single-degenerate" scenario. However, a white dwarf accreting from a relatively low mass companion via a sufficiently high efficiency (>60%-80%) Roche lobe overflow is still consistent with our limits. The "double-degenerate" merger scenario also cannot be excluded.