It is energy-consuming and operationally cumbersome for all users to continuously estimate the channel quality before each data transmission decision in opportunistic scheduling over wireless fading channels. This observation motivates us to understand whether and how opportunistic gains can still be achieved with significant reductions in channel probing requirements and without centralized coordination amongst the competing users. In this work, we first provide an optimal centralized probing and transmission algorithm under the probing constraints. Noting the difficulties in the implementation of the centralized solution, we develop a novel Sequential Greedy Probing (SGP) algorithm by using the maximum-minimums identity, which is naturally well-suited for physical implementation and distributed operation. We show that the SGP algorithm is optimal in the important scenario of symmetric and independent ON-OFF fading channels. Then, we study a variant of the SGP algorithm in general fading channels to obtain its efficiency ratio as an explicit function of the channel statistics and rates, and note its tightness in the symmetric and independent ON-OFF fading scenario. We further expand on the distributed implementation of these greedy solutions by using the Fast-CSMA technique.