As a Scot, I've got to go for Colin Montgomerie. He won the European Tour money list SEVEN YEARS in succession between 1993-1999; He won 28 European Tour events in the 90's and two more wins outwith Europe; He performed magnificently for Europe in several Ryder Cups, remaining unbeaten in the singles.
Many think of Monty as a failure simply because he hasn't got a major championship under his belt. He was however narrowly beaten in 2 (or possibly 3) U.S. Open/USPGA play-offs. One of those defeats only came about when Steve Elkington drained a monster putt to join him in the play-off. As Monty himself said, over 72 holes no-one beat him in those events.