"Death sentence" and "death penalty" were equally common names for the capital punishment of execution — the state-sanctioned death of an individual in recompense for crimes of an especially grave nature, such as murder or treason. Sometimes, especially in Earth's past, or in places without clear governmental structures, it could be carried out against people for less profound crimes, or even arbitrarily.
Earth
On Earth, it was a divisive issue. Some parties, such as the Briton, Professor Kettering, believed that the death penalty was a backwards conception of justice. (DW: The Mind of Evil) To the contrary, many Americans in Jacksonville, Kentucky on "Miracle Day" fully believed that the rapist and murderer Oswald Danes should not have been paroled after his death by lethal injection failed. (TW: The New World)
Indeed, there was a general divide between the British and American viewpoints on the issue. The death penalty was abolished in the United Kingdom at least by the late 20th century, whereas it was still an acceptable punishment in at least the state of Kentucky as late as the year 2011. (DW: The Mind of Evil, TW: The New World)
At the time of World War I, however, shell-shocked Tommy Brockless was killed by a British firing squad for cowardice. (TW: To the Last Man)
Centuries before, one of the factions angling to succeed to the duchy of San Martino sanctioned the beheading of the Fourth Doctor. (DW: The Masque of Mandragora)
In the 16th century, the nine-day queen, Lady Jane Grey was quietly executed by the new queen, Mary I at the Tower of London, following months of Jane being locked up. (SJA: Lost in Time, VD: The Nine-Day Queen) Later, following a performance of William Shakespeare's Love's Labour's Won in the Globe Theatre, Mary's sister, Elizabeth I called for the Tenth Doctor's head, but the Doctor escaped in his TARDIS. (DW: The Shakespeare Code)
Elsewhere
Elsewhere in the universe, the death penalty was known to be used by the Raxacoricofallapatorians. The Slitheen family, for instance, were tried and sentenced to death in absentia. The Ninth Doctor, who had captured Blon Fel-Fotch in Cardiff and wanted to extradite her back to Raxacoricofallapatorius, was therefore faced with the moral dilemma of whether he could become, in effect, her executioner. (DW: Boom Town) Later, in 2009, members of the Slitheen-Blathereen family apprehended two other Slitheen, teleporting them on board their ship to send to Raxacoricofallapatorius. Other members of the Slitheen were said to have been "brought to justice". (SJA: The Gift)
On the Moon, the Judoon quckly tried a human inside the H2O Scooped Royal Hope Hospital for assault, executing him on the spot. (DW: Smith and Jones)
Time Lords exercised the death penalty, largely for crimes against the Laws of Time. The penalty for setting one's self up as a god in a more primitive civilisation, for instance, was vapourisation. (BFA: False Gods) The death penalty on Gallifrey was sometimes effected through a so-called "Warrant of Termination", such as was served on the Fifth Doctor. In that instance, however, he wasn't threatened with death because of any actual wrongdoing, but because he had become controlled by a malevolent entity that posed a grave risk to the entire universe. (DW: Arc of Infinity) Later, the Fifth Doctor and Peri were nearly executed by firing squad on the planet Androzani Major by the authority of the quasi-governmental Sirius Conglomerate. (DW: The Caves of Androzani)
As part of an agreement, the Master was sent to Skaro by the Time Lords and subsequently tried and executed by the Daleks, though he survived in the body of a Deathworm. (DW: Doctor Who, EDA: The Eight Doctors) Similarly, the being known as the Wire evaded its physical execution by transferring its consciousness into electrical energy. (DW: The Idiot's Lantern)
