The Nobel Scientific Background paper is the best introduction to all of these people, and a good introduction to mechanism design in general.
His most cited paper is on auction design. He laid out basic results for how to use auctions to extract revenue and elicit information about the value of the good. These results have informed numerous privatizations and auction schemes in the last twenty-five years.
Here is a very important paper, with David Baron, on how to regulate a monopolist with unknown costs. Strict marginal cost pricing is no longer possible. Under some assumptions, allow the monopolist to charge a relatively high price, but design penalties to elicit an honest reporting of costs. The key point of course is that monopolists won’t always report their costs truthfully. This is one of the most important papers in regulatory economics in the last thirty years and it has helped disillusion many economists with a narrow ideal of marginal cost pricing.
Myerson also has important papers on how social choice theory is linked to bargaining theory, and which social choice procedures are most likely to elicit truthtelling.
I think of his "Mechanism Design with An Informed Principal" as one of his most important papers, though Google Scholar does not concur. Let’s say that a principal knows something an agent does not and wishes to maintain that information asymmetry. How can a principal construct the best incentive scheme for the agent? The problem is, choosing the scheme itself may reveal information to the agent and thus eliminate the principal’s advantage. Myerson showed what solutions to this problem have to look like. This is a very clever problem and a very elegant paper.
Among the current research papers you will notice a strong interest in public choice and institutions, though Myerson is not usually thought of as applied, nor is that where his influence has come. Electoral rules, corruption, and political institutions all are commanding his attention.
Here is an interview with Myerson on game theory. Here is Myerson’s take on the core problems of social choice theory, a summary of the theoretical side of the field.
Here is Myerson on Hurwicz, which is also a very good introduction to Hurwicz.
Off the beaten track, here is Roger Myerson on Thomas Schelling’s Strategy of Conflict. Here is Myerson’s Op-Ed draft on why America should accept limits on its military power, namely to limit deadly rivalries. Here Myerson recommends federalism for Iraq.