Chewing gum or bubble gum was a flavored Earth concoction, which Humans chewed but did not consume.
In the 20th century, a stick of bubble gum – a special variety, popular among children, in which the chewed gum could be blown into a bubble – was usually included with a pack of baseball cards - the 24th Century trader Kivas Fajo, whose massive collection of artifacts included a 1962 Roger Maris card, made sure that the scent of the gum originally packaged with it was preserved inside its display case. (TNG: "The Most Toys")
In 1957, Johnnies Market in Carbon Creek had a chewing gum vending machine outside its door, offering two varieties. (ENT: "Carbon Creek")
One of the Enterprise bingo challenges was using the transporter to reflavor gum. (SNW: "Spock Amok")
An antique shop in San Francisco in 1986 contained a number of chewing gum vending machines. (Star Trek IV: The Voyage Home)
Chewing gum was also a habit on Sigma Iotia II in 2268, where the planet's society was based on the 1920s gangster world of Earth. (TOS: "A Piece of the Action")
In 2364, Beverly Crusher was offered chewing gum in a Dixon Hill holodeck program, but mistakenly swallowed it. (TNG: "The Big Goodbye")
Guinan was chewing on chewing gum when she appeared as Gloria from Cleveland in the Dixon Hill holodeck program in 2367. (TNG: "Clues")
One of the lots sold in an auction held by Quark in 2373 was a mint condition 1951 Willie Mays rookie baseball card, but it did not come with the original packaging or chewing gum. (DS9: "In the Cards")
In 2375, during a game of baseball in the holosuite, Julian Bashir was confused by the notion of a food that one simply chews. Miles O'Brien gave Bashir a piece of his custom-made, replicated chewing gum that was infused with the flavor of Scotch whisky. (DS9: "Take Me Out to the Holosuite")
In 2377, Tom Paris and Ensign Tabor created a holodeck program of the Palace Theater complete with authentic chewing gum stuck to the floor. When she stepped on a piece, B'Elanna Torres opined that there was "such a thing as too much authenticity". (VOY: "Repression")
A deleted scene from SNW: "Charades" had Human Spock trying chewing gum, speculating on whether to combine it with nuts or a pickle. [1]