Spanking
Spanking was an ancient form of punishment given on Earth to Human children, by striking them on the buttocks, for misbehaving. 

In 2268, when the Dohlman Elaan warned Captain James T. Kirk never to touch her again, Kirk responded with a warning of his own, with regards to her tantrum like behavior, remarking that "if I touch you again, Your Glory, it'll be to administer an ancient Earth custom called a "spanking," a form of punishment administered to spoiled brats." ()

In the 2270s, when Spock established that V'ger was merely a child, and as such, should be treated as a child, Leonard McCoy reacted to Spock's understatement, exclaiming, "that thing is about to wipe out every living thing on Earth, now what do you suggest we do? Spank it?" ()

In Reginald Barclay's 2366 holodeck fantasy, his hologram of Beverly Crusher warned the hologram of her son Wesley Crusher to mind his manners and not embarrass her in front of their guest, the "real" Geordi La Forge, warning that "Master Barclay will spank you if you misbehave." () 

During the first half of the 24th century, some Human parents still punished their children with spanking, at least occasionally. Miles O'Brien said he got his bottom whacked by his dad once or twice. ()

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Punishments