In this paper, we identify sufficient conditions under which static teams and a class of sequential dynamic teams admit team-optimal solutions. We first investigate the existence of optimal solutions in static teams where the observations of the decision makers are conditionally independent or satisfy certain regularity conditions. Building on these findings and the static reduction method of Witsenhausen, we then extend the analysis to sequential dynamic teams. In particular, we show that a large class of dynamic LQG team problems, including the vector version of the well-known Witsenhausen's counterexample and the Gaussian relay channel problem viewed as a dynamic team, admit team-optimal solutions. Results in this paper substantially broaden the class of stochastic control and team problems with non-classical information known to have optimal solutions.