Several episodes of Trek have been censored or simply not shown over the years. Assuming your question relates to the UK, then four instances are notable;
TOS : The Empath, Whom the Gods Destroy, Plato's Stepchildren and Miri were all removed from the broadcast schedule for over 10 years due to containing subjects of "madness, torture, sadism and disease" in a show that the BBC considered to be intended for children.
Additionally, "violent images" were removed from certain episode including TNG: "Conspiracy" (showing the aftermath of Remick being shot with phasers by Picard and Riker), TNG: "The Icarus Factor" (in which Worf is repeatedly hit with Klingon 'painstiks') and the removal of a line from "The High Ground" which relates to Irish reunification.
