Wow, I don't know where to begin.
First, since the thread says the 20th century, to even mention Tiger Woods or Federer is crazy. Jack Nicklaus is clearly the best golfer up till 1999, and you would also have to put Palmer, if not Hogan ahead of Woods in the 20th century. Even counting to the present, sure Woods and Federer are most likely going to break each sports' record for majors. But what if they don't win anymore majors somehow? Are they still better than Nicklaus and Sampras? Of course not.
Other people have been mentioning one sport people, and either saying how much they accomplished and dominated that sport, or have been arguing how famous or far reaching across the globe they were. Well by this criteria, you have to mention George Herman Ruth, better known as the Babe.
Not only did he tear it up as probably the best left-handed pitcher ever up until the time he stopped pitching, but he totally dominated with his bat. The league leaders in homers were often single digits, or just over. Ruth's last year in Boston, when they let him play rightfield when he wasn't pitching, he set the all time record with 29 homers. His next year, his first as a Yankee, he hit 54 almost doubling his own record, which he did do the next year, hitting 59 homers. He also out homered every other entire team in the majors those years. The Babe even outhomered some teams 7 years later when he set the record again with 60.
Ruth saved the game after the 1919 Black Sox scandal, and kept it the most popular sport in America, which it stayed, until the mid 50's. But he was easily the first true sport celebrity. Babe Ruth lived life large. He hung out and partied with movie stars, gangsters, and high level politicians. He was the first athlete to make a higher yearly salary then the president. When asked about this, Ruth said he deserved it, as he had a better year. He endorsed everthing under the sun, and was the first athlete to be more popular endorsing products than movie stars.
Ruth was routinely in the news on the radio, newsreels at the theaters, and in the headlines of every paper , without even doing anything on the field. Either he was caught carousing with strippers or gangsters, or he was donating his money and time to underpriveled or sick children, And with no internet or television, people knew who were Babe Ruth was around the globe. During WW2, more than 5 years after he retired, Japanese soldiers would yell " To hell with Babe Ruth " as they would attack the allied forces.
In short, Babe Ruth was Jordan and Tiger, about 6 or 7 decades before them.