It's an accomplishment to get into all four of the men's golf major championships in a single golf season. It's hard to get into the Masters, US Open, British Open Championship and PGA Championship in a calendar year. It's an even bigger deal to make the cut in all four major championships in a year, placing you in the company of usually less than 15 golfers in a year who played all 16 major rounds in a year.
So, what Jack Nicklaus and Tiger Woods have accomplished in making 39 consecutive major championship cuts is absolutely astounding. They share the record for the most consecutive cuts made in major championships.
Jack Nicklaus made 39 consecutive major championship cuts from the 1969 Masters through the 1978 Open Championship (which he won). Nicklaus then made his next 12 major cuts, by the way.
Tiger Woods made 39 consecutive major championship cuts from the 1996 US Open, where he was low amateur, through the 2006 Masters. He missed the cut at the 2016 US Open, his first missed major cut as a pro and his first major after his father Earl died. He made his next 10 major cuts, including four wins, after that missed cut at Winged Foot.
Gary Player made 37 consecutive major cuts from the 1970 PGA Championship through the 1980 Masters. He didn't play in the 1973 Masters.
Ben Hogan made 35 consecutive major cuts, though his streak comes with the caveat that the PGA Championship was a match-play affair until 1958 and that he didn't play in all four majors each season.
Steve Stricker owns the current active major championship cuts-made streak at 26, through the 2017 PGA Championship. That streak matches the longest by Arnold Palmer.