It’s a salt of the Earth, unpretentious name that’s also tough and a little daring. When an audience finds out a character is named Jack, I think they get a pretty consistent impression of him. Some names are like that; others don’t carry as many associations.
Not always, especially in the South.
My friend Jack, who’s from south Georgia (by which I mean the southern part of my home state, not this place), has a brother named John.
When Jack lived in New Jersey he had to keep correcting people who called him “John” in more formal settings.
My Dad used to say, “Every Tom, Dick, and Harry’s named John.” He could say that because his name was John. It would have been my name, too, had I been male.
And Webster’s New World Dictionary (paperback) has “a man or boy” listed as the first definitioin of jack. Heck, it’s even one of a card suit’s face cards, along with the king and queen. So I think we can say that Jack means Man, and not a gentleman.
There’s an English expression “Jack-the-lad”, as in “E’s a right Jack-the-lad, that one”: the implication is of a lady’s man, a raffish scoundrel of slightly unscrupulous but admirable daring. As to “Jack” being a generic term for “man”, well, there’s also “jack in the box” and “every man jack”.
Scissorjack
Shoulda previewed: I see the last one’s already been covered. There are also however “steeplejacks” and “jack-o’-lanterns”. As for ship’s captains, there’s also “Calico” Jack Rackham in G. M. Fraser’s The Pyrates.
Bump. I’m forgetting Captain Jack Absolute, initially a character in Sheridan’s The Rivals and latterly the star of his own rather good {if a little Flashmanesque} historical swashbucklers by C. C. Humphreys.
It’s a good topic to bump up on Talk Like a Pirate Day.
And Captain Jack “Half-cocked” Shaftoe from Neal Stephenson’s Baroque Cycle.
Just for the record, the name Andrew actually does come from the Greek word for man (or ‘manly’), ανδρος or andros.
The same root is part of the name Alexander, which means ‘protector of man’.
My grandfather’s first and last name were both derivations of the name Alexander, so his name actually means ‘defender of man, defender of man’.
Funny, this is not the first time the Jack discussion has come up. From Notes and Queries issue 179, 1853 at Project Gutenberg I give you way to much information. I guess what goes around comes around.
Actually a misquote. William Manchester wrote that JFK called out to his son in another room, and, receiving no reply, immediately repeated the name. A reporter nearby overheard and wrote that the son’s nickname was “John-John.” It wasn’t.
My eldest son’s named John - named after his grandfather.
We would be remiss not to also point out “jackleg” in the sense of “amateur”, an ordinary fellow doing something he is not professionally trained to do–a jackleg carpenter, for instance.
I would submit that “Jack” is not derived from a term for a man, but rather that it was so common a name that it became used to refer to any otherwise unnamed man or boy. From there, it took on many of the myriad meanings we’ve seen in this thread.
Why should you listen to me, though? It’s not like I know jack about it. 
Was he referring to the real-life pirate?
There was also “Dancing Jack” Duvall, whom I know from Peter S. Beagle’s song “The Ballad of Mary Read” (for some reason I can’t seem to find the lyrics online anywhere). I think he was a real-life pirate; I know Mary Read was, but the wiki article on her mentions only Jack Rackham.
Where does Jack Shit fit in?
Very loosely, but yes: Fraser’s very thorough when it comes to his historical homework.
Nobody knows.
My dad is named John, and one of his brothers is named Jack. Jack is the youngest of five children, and my grandparents let the other four decide what to name the newest baby.
Theres the saying "I’m all right Jack"used sarcastically in the U.K. to make somebody aware that they’re being selfish.