Well... it depends on what metric you use. Total # of second place finishes goes to the Golden Bear by a nose (58 to Sam Snead's 57).
But if you measure who took second the most by frequency of second place finishes you certainly have to bestow the honor upon Harold McSpaden. Harold not only holds the record for most unfortunate golf career, he holds the record for most 2nd place finishes in a single year. With 13 second place finishes in 1945, one can only imagine the number of silver medals he had stacked in his closet shoebox.