Has anybody ever played all three major US sports professionally and how many have played two of the three?

Luke Urban is one example.

Luke Urban did it all. Football, basketball, baseball, hockey… Sure, a lot of athletes play more than one sport, and many play more than one at a high level. But Urban was able to letter in four sports at his alma mater, Boston College, and play professionally at two, football and baseball. Some seven decades before such modern-day two-sport athletes as Bo Jackson and Deion Sanders captivated fans with their legendary feats, Urban traversed diamonds and gridirons with none of the notoriety and a fraction of the earnings.

More of his remarkable achievements here:

http://www.angelfire.com/retro/urbanstory/

Clearly he was the Bo Jackson of his day!

Actor Chuck Connors (of "The Rifleman" fame) played both pro basketball (with the Boston Celtics) and pro baseball (with the Brooklyn Dodgers and the Chicago Cubs).

https://en.wikipedia.org/wiki/Chuck_Connors

The aforementioned Deion Sanders was also a two-sport player, playing pro football for five different teams and pro baseball for five different teams. He's also the first person in major North American sports to hit a homerun and score a touchdown in the same week.

https://en.wikipedia.org/wiki/Deion_Sanders

The aforementioned Bo Jackson spent three years with the Raiders (1987-90) and eight seasons in pro baseball with the Royals, White Sox and Angels. In 1989, he hit a mammoth homerun in the All-Star Game and earned game MVP honors.

https://en.wikipedia.org/wiki/Bo_Jackson

Brian Jordan spent two seasons as an Atlanta Falcon before concentrating full-time on baseball. He enjoyed a 14-year major-league career that included two stops in Atlanta and an All-Star selection in 1999.

https://en.wikipedia.org/wiki/Brian_Jordan

It looks like the answer is no. To the best of my knowledge and research, no one has 'PLAYED' all three major professional sports (MLB, NFL & NBA) at a Major League level. College sport doesn't answer that part of the question. As far as two sport...there is also Gene Conley who played for the Phillies and Celtics. Maybe the question refers to the New York organist who played for all the teams there and whose name slips my mind.

Jim Thorpe

Thorpe signed with the New York Giants baseball club in 1913 and played sporadically with them as an outfielder for three seasons. After playing in the minors with the Milwaukee Brewers in 1916, he returned to the Giants in 1917, but was sold to the Cincinnati Reds early in the season...etc.

Thorpe played football for Canton from 1915 through 1920. He also played 52 NFL games.

Thorpe continued to be active in sports. By 1926 he was the primary draw for the "World Famous Indians" in LaRue, which sponsored traveling football, baseball, and basketball teams. A ticket discovered in an old book in 2005 only recently brought to light his career in basketball. "Jim Thorpe and His World-Famous Indians" barnstormed for at least two years (1927–28) in parts of New York, Pennsylvania, and Marion, Ohio. Although pictures of Thorpe in his WFI basketball uniform were printed on postcards and published in newspapers, this period of his life was not well documented. Until 2005 most of Thorpe's biographers were unaware of his basketball career.

NOTE: May not have been NBA, but WAS Pro!

https://en.wikipedia.org/wiki/Jim_Thorpe#Baseball.2C_football.2C_and_basketball