Vaporisation was an execution method provided for by law on Gallifrey. It was performed in a vaporisation chamber.
It was applied for the murder of the Lord President. For example, the Fourth Doctor, framed by the Decayed Master for the death of the President, was threatened by this kind of death sentence. The Doctor believed vaporisation without legal representation were against the Constitution. (TV: The Deadly Assassin)
Vaporisation was also the penalty for setting oneself up as a god in a more primitive civilisation. (AUDIO: False Gods)
Vaporisation was also practised in the Earth Empire in the 26th century. Condemned criminals were offered the choice of vaporisation or becoming a Dalek Killer. (COMIC: Abslom Daak... Dalek Killer)
Similar techniques
By the time of Borusa's presidency, ordinarily it wasn't made provision for executions, except for severe cases threatening collective security, in which molecular dispersal was the employed method. (TV: Arc of Infinity)