A few months ago I would have said Tiger Woods, however, that was assuming he would continue as he had done winning majors and tournaments and pass Jack Nicklaus. However, there is now a huge question mark over his future so it would have to be Jack Nicklaus, with 18 major wins.
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Tough question, and the answer is a matter of opinion. Jack Nicklaus won 18 majors, and that is generally regarded as the most important milestone to reach. Jack's greatness has stood the test of time. On the other hand, Tiger Woods has had a remarkable career, and he still may break Jack's record. I grew up watching Jack, on TV and live at tournaments. I was inspired by him. I figured that, on any given day, I could put together that one great round. There was nothing he did on any particular shot that I couldn't do. He was great because he could put it all together, all the time. Tiger, on the other hand, does things that no human being can do - like hit an 8 iron out of deep rough, 190 yards over water into a tight green, and put it next to the hole. All of this, of course, is not based on his recent performance. Time will tell if the record books will show him as the greatest.
There are many other greats, such as Bobby Jones, Ben Hogan, Arnold Palmer, etc. that some will say are in the same category. However, I believe that Jack and Tiger have redefined the game more than any other golfer, before or since.