In practice, one is not only interested in the qualitative characterizations provided by Lyapunov stability, but also in quantitative information concerning system behavior, including estimates of trajectory bounds, possibly over finite time intervals. This type of information has been ascertained in the past in a systematic manner, using the concept of practical stability. In the present paper we establish new sufficient conditions for practical stability of an important class of switched systems. As in the classical Lyapunov theory, our results constitute a direct method, making use of auxiliary scalar-valued Lyapunov-like functions. These functions, however, have properties that differ significantly from the usual Lyapunov functions. We demonstrate the applicability of our results by means of several specific examples.