Space suit

A space suit, alternatively spelt spacesuit, (PROSE: Diamond Dogs) was an article of protective clothing developed for space travel. They were needed to breathe in outer space, although beings possessed by the Beast were capable of surviving without them. (TV: 42, The Impossible Planet)

Earth space suits were created sometime prior to 1969 by the humans, possibly under the guidance of the Silence. (TV: The Impossible Astronaut, Day of the Moon)

The Doctor's space suits
In order to take a walk on the Moon, the Second Doctor provided for himself and his companions white suits, with transparent helmets, taken from "the chest" of the TARDIS. (TV: The Moonbase) Jamie McCrimmon and Vorac wore the spacesuits to ride the time winds. (PROSE: Undercurrents) The Sixth Doctor wore the same space suit while he was exploring the Axos ship — the one with the "fish bowl helmet". (AUDIO: The Feast of Axos)

Whilst fighting the Beast on Sanctuary Base 6 in the year 43K2.1, the Tenth Doctor acquired an orange space suit, which he used to explore the depths of the Beast's prison, a deep pit. He left the base with the suit on. (TV: The Impossible Planet, The Satan Pit)

The Doctor wore a similar suit when battling Torajii in the 42nd century. He needed it to temporarily exit the SS Pentallian. (TV: 42)

The Doctor kept his Sanctuary Base 6 space suit in the TARDIS. He wore it to stroll on the surface of Mars in 2059. The helmet was damaged in the escape from Bowie Base One, and abandoned shortly after. (TV: The Waters of Mars)

The Eleventh Doctor later again wore the orange space suit, having replaced the helmet and removed the Sanctuary Base 6 insignia, when he travelled to a newly-formed Earth. He thought it brought out his eyes, although Clara Oswald noted that it made her eyes hurt. (TV: Hide)

Many centuries later, the Twelfth Doctor, by this time, had acquired two more orange spacesuits which he lent to Clara and Courtney Woods so they could all go for a quick moonwalk. (TV: Kill the Moon)

Later still, the Thirteenth Doctor and her companions would use these suits to respond to a distress call from a space train. In the process Dan Lewis's helmet was shot, shattering the face plate, briefly exposing him the vacuum of space. This brush with death caused him to lose his desire to continue traveling with the Doctor. (TV: The Power of the Doctor)

"The Impossible Astronaut" space suit
When the Silence needed space suits, they implanted the idea of travelling to the Moon in the minds of the humans. They then trapped Melody Pond in a modified suit that they'd stolen from the space program; it served as an exoskeleton for her. They put twenty different kinds of alien technology in it, and the space suit was capable of operating without its inhabitant. When the Eleventh Doctor, River Song, Amy Pond and Rory Williams arrived, Melody escaped from the bonds of the suit, destroying it in the process. The suit processed sunlight directly, had built-in weaponry, and a communications system that could hack into anything, including the telephone network. River Song even claimed that you didn't have to eat with it on. (TV: Day of the Moon)

River was again abducted by the Silence and placed in another space suit. She sat submerged in the waters of Lake Silencio, before rising out of it and "killing" the Doctor. (TV: Closing Time, The Wedding of River Song)

Other space suits
Time traveller Orson Pink possessed a Sanctuary Base Six orange spacesuit. (TV: Listen)

The crew of Chasm Forge used smartsuits. Upon arriving on the mining station, the Twelfth Doctor, Bill Potts and Nardole also wore the suits. (TV: Oxygen)