Given a metric space , a weighted graph over is a metric -spanner of if for every , , where is the shortest path metric in . In this paper, we construct spanners for finite sets in metric spaces in the online setting. Here, we are given a sequence of points , where the points are presented one at a time (i.e., after steps, we see ). The algorithm is allowed to add edges to the spanner when a new point arrives; however, it is not allowed to remove any edge from the spanner. The goal is to maintain a -spanner for for all , while minimizing the number of edges, and their total weight. We construct online -spanners in the Euclidean -space, -spanners for general metrics, and -spanners for ultrametrics. Most notably, in the Euclidean plane, we construct a -spanner with competitive ratio , bypassing the classic lower bound for lightness, which compares the weight of the spanner to that of the minimum spanning tree.