In this paper, we exploit channel diversity for opportunistic spectrum access (OSA). Our approach uses channel quality as a second criterion (along with the idle/busy status of the channel) in selecting channels to use for opportunistic transmission. The difficulty of the problem comes from the fact that it is practically infeasible for a CR to first scan all channels and then pick the best among them, due to the potentially large number of channels open to OSA and the limited power/hardware capability of a CR. As a result, the CR can only sense and probe channels sequentially. To avoid collisions with other CRs, after sensing and probing a channel, the CR needs to make a decision on whether to terminate the scan and use the underlying channel or to skip it and scan the next one. The optimal use-or-skip decision strategy that maximizes the CR's average throughput is one of our primary concerns in this study. This problem is further complicated by practical considerations, such as sensing/probing overhead and sensing errors. An optimal decision strategy that addresses all the above considerations is derived by formulating the sequential sensing/probing process as a rate-of-return problem, which we solve using optimal stopping theory. We further explore the special structure of this strategy to conduct a "second-round" optimization over the operational parameters, such as the sensing and probing times. We show through simulations that significant throughput gains (e.g., about 100%) are achieved using our joint sensing/probing scheme over the conventional one that uses sensing alone.