"...not everybody keeps their genitals in the same place."
Human genitals
Goss bragging it up
Censored Boimler's genitals
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A hologram of Brad showing off his censored penis and testicles
The genitals or sexual organs were the reproductive organs in most humanoid species. In the Human species, the males and females had different sexual organs. (TNG: "The Outcast")
The fact that different humanoid species can interbreed implies that most humanoids had distinct male and female sexual organs. A notable exception were the J'naii.
In males, the testes were very sensitive to pressure. A sharp blow to the organ could render males of at least three known species helpless: Human, Klingon and Orion. (Star Trek III: The Search for Spock; ENT: "Bound")
In at least one species, the genitals were located in the right knee. While different from many other species, this did not affect the sensitivity of the organ. (Star Trek VI: The Undiscovered Country)
During his visit aboard the USS Enterprise-D in 2366, DaiMon Goss implied the size of his "sex organ" with a revealing gesture to Ensign Bailey while attempting to engage her in Ten Forward. (TNG: "The Price")
As there was no audible dialogue, this information was not immediately evident, and was more explicitly revealed in the Star Trek: The Next Generation Companion, 2nd ed., p. 109.
When Chief Miles O'Brien made an unsuccessful attempt to retrieve his time lost daughter Molly from Golana, he said "bollocks," which was a profane term used to describe the testicles. (DS9: "Time's Orphan")
Jadzia Dax had her ovaries operated on in an attempt to be able to conceive with Worf. (DS9: "Tears of the Prophets")
DIS writers Bo Yeon Kim and Erika Lippoldt intended Klingon males to naturally have two penises. [1]
In 2380, Ensign Brad Boimler was caught with exposed genitals by Beckett Mariner on Orbital Platform Gamma while he was waiting for his girlfriend, Lieutenant Barbara Brinson. (LD: "Cupid's Errant Arrow")
In 2381, Ensign Beckett Mariner was forced to kick Commander Jack Ransom in the groin, which she referred to as his "Neutral zone", to disable him and save the USS Cerritos from his strange energy-induced attacks. (LD: "Strange Energies")
Later that same year, Mariner participated in a Simulator holopod program mimicking a Polywater intoxication incident leading to the entire crew naked with one incident showing Boimler with his legs raised and his genitals exposed. (LD: "I, Excretus")