The Gibbard-Satterthwaite Impossibility Theorem holds that dictatorship is the only Pareto optimal and strategyproof social choice function on the full domain of preferences. Much of the work in mechanism design aims at getting around this impossibility theorem. Three grand success stories stand out. On the domains of single peaked preferences, of house matching, and of quasilinear preferences, there are appealing Pareto optimal and strategyproof social choice functions. We investigate whether these success stories are robust to strengthening strategyproofness to obvious strategyproofness (OSP), recently introduced by Li (2015). For single peaked preferences, we characterize the class of OSP-implementable and unanimous social choice functions as dictatorships with safeguards against extremism - mechanisms (which turn out to also be Pareto optimal) in which the dictator can choose the outcome, but other agents may prevent the dictator from choosing an outcome that is too extreme. Median voting is consequently not OSP-implementable. Indeed, the only OSP-implementable quantile rules choose either the minimal or the maximal ideal point. For house matching, we characterize the class of OSP-implementable and Pareto optimal matching rules as sequential barter with lurkers - a significant generalization over bossy variants of bipolar serially dictatorial rules. While Li (2015) shows that second-price auctions are OSP-implementable when only one good is sold, we show that this positive result does not extend to the case of multiple goods. Even when all agents' preferences over goods are quasilinear and additive, no welfare-maximizing auction where losers pay nothing is OSP-implementable when more than one good is sold. Our analysis makes use of a gradual revelation principle, an analog of the (direct) revelation principle for OSP mechanisms that we present and prove.