In my opinion, the 1937 paper on the theory of the firm is his best. It's a simple, powerful observation. It's one of the most cited papers in economics, but starting with Alchian and Demsetz's (excellent) 1972 paper, economists working on the theory of the firm have actually moved away from Coase's view of the firm. According to Coase, firms and markets are alternate methods of coordinating resources. So coordination is the central role of the firm. Modern theories of the firm, however, tend to view firms as contractual arrangements that solve some incentive problem. These theories do not feature a coordination problem at all. The allocations are all well known in these models, so no coordination is required. Firms are simply contractual arrangements between parties that solve incentive problems. My second year paper on the theory of the firm argued that the coordinating role is the primary function of the firm. I tried to show how entrepreneurs attempting to coordinate pieces of the economy will end up creating the special contractual arrangements that we call firms.
I'll end with a personal anecdote: Since I'd written a paper more aligned with Coase's coordinating story, I thought I should send it to him. His office was nearby at the University of Chicago Law School, so I decided to swing by and drop it off. He wasn't in, but his research assistant was. I left the paper with the assistant along with a note. A few months later, an envelope personally addressed by Coase in old-fashioned cursive handwriting arrived in the mail. The letter inside--also handwritten--informed me that the great man was not currently working on the theory of the firm but would return to the topic in the future and would read it when he did. I admired his optimism. He must have been 93 at the time!
RIP, Professor Coase.
Here's a summary about Coase's contributions.