For every integer n and evrery positive real number r > 0 and a Radon random vector X with values in a Banach space E, let e_{n,r}(X,E) = inf{(E (\min_{a \in \alpha} || X-a ||^r )^{1/r}}, where the infimum is taken over all subsets \alpha of E with card(\alpha) <= n (n-quantizers). We investigate the existence of optimal n-quantizers for this L^r-quantization propblem, derive their stationarity properties and establish for L^p-spaces E the pathwise regularity of stationary quantizers.