[en] We present numerical results for the one-dimensional symmetric Kondo lattice, obtained by using a lattice-fermion Monte Carlo algorithm in conjunction with recently developed low-temperature stabilization techniques. The results are extrapolated in imaginary-time increment and lattice size to obtain controlled estimates for various quantities in the thermodynamic limit. In particular, we compare spin correlations with Ruderman-Kittel-Kasuya-Yosida predictions and two-impurity data, and note the opening of a gap as the temperature is lowered. We next discuss certain properties of the frequency-dependent conductivity, and compare ground-state results with a strong-coupling expansion. We then perform a particle-hole transformation to obtain an ''attractive-J'' lattice and discuss the existence of superconductivity in such a model. Finally, we discuss the relevance of our results to various theoretical treatments of Kondo and Anderson lattice models