Here are the best players who have never won a major, as of July 2018.
Major Appearances: 79
Lee Westwood has played in 79 majors, made 61 cuts, has 18 top-10 finishes, and 11 top-5 finishes.
It’s hard to single out Westy’s best year because between 2009 and 2013 he finished in the top 10 in at least two majors every year, but in 2010 he finished second in both the Masters and Open Championship.
With two PGA Tour wins and 23 European Tour wins tacked onto his ridiculous major results, Lee Westwood is one of the best golfers who has never won a major.