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][1], [Whom the Gods Destroy][2], [Plato's Stepchildren][3] and [Miri][4] 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.

![BBC letter][5] 

Additionally, "violent images" were removed from certain episode including TNG: "[Conspiracy][6]" (showing the aftermath of Remick being shot with phasers by Picard and Riker), TNG: "[The Icarus Factor][7]" (in which Worf is repeatedly hit with Klingon '[painstiks][8]') and the removal of a line from "[The High Ground][9]" which relates to Irish reunification.

![Worf hit with Pain Sticks][10] ![Remick aftermath from Icarus Factor][11]


  [1]: http://en.memory-alpha.org/wiki/The_Empath_%28episode%29
  [2]: http://en.memory-alpha.org/wiki/Whom_Gods_Destroy_%28episode%29
  [3]: http://en.memory-alpha.org/wiki/Plato%27s_Stepchildren_%28episode%29
  [4]: http://en.memory-alpha.org/wiki/Miri_%28episode%29
  [5]: https://i.sstatic.net/d7R8l.jpg
  [6]: http://en.memory-alpha.org/wiki/Conspiracy_%28episode%29
  [7]: http://en.memory-alpha.org/wiki/The_Icarus_Factor
  [8]: http://en.memory-alpha.org/wiki/Painstik
  [9]: http://en.memory-alpha.org/wiki/The_High_Ground_%28episode%29
  [10]: https://i.sstatic.net/Q3XXm.jpg
  [11]: https://i.sstatic.net/fBS3S.jpg