Even though I don't personally believe in it, reincarnation is a fact in the Toobworld Dynamic. Many times it's not just the soul that is "born to rerun" but the physical form as well (which can happen independently of the soul's return.) And this is not limited to just the inhabitants of Earth Prime-Time - the souls of aliens can be reborn into humans and vice versa.
(The Minbari believed in this; they thought their souls could be reborn in Terrans, which is why they stopped the war with Earth. But as events at the 'Babylon 5' space station later showed, this was not the case.)
The planet Mondas used to be the twin of Earth Prime-Time, sharing its orbit and looking much like the younger planet... only upside down. (Mondas - which means "Earth" in Old Gallifreyan and other ancient languages - was created by God; Earth Prime-Time was an artificial computer. It was built by the Magratheans, who - according to 'The Hitch-Hiker's Guide To The Galaxy', specialized in planet-building.)
Mondas existed long before Earth Prime-Time came into being and it vanished from the solar system around the same time as Mankind was getting a toe-hold on the other big blue marble. Its inhabitants were basically humanoid - until they traded in their bodies for metallic form.
And it's my contention that several of the people of Mondas were reincarnated on Earth.
I have two examples of reincarnation in which the mind and body were reunited from one world to the next, both of them from the distant past of Mondas, when the Seven Kingdoms were in power on the continent of Westeros. And both of them involve the same two shows.
1] JOJEN REED > TIMOTHY LATIMER
Jojen Reed of Mondas was gifted with greensight, which gave him prophetic dreams. It was his dream of a three-eyed raven trying to free a chained wolf which sent him seeking out Bran and Rickon Stark of Winterfell.
He was reborn on Earth as Timothy Latimer in the Norfolk region of England in the late 1800s. Latimer also had a form of second sight, which he was able to use in helping the Time Lord known as the Doctor to defeat the Family of Blood.
'Game Of Thrones'
'Doctor Who' - "Family Of Blood" & "Human Nature"
2] SER DAVOS SEAWORTH > CAPTAIN ZHUKOV
Davos was a sea captain and a smuggler known as the Onion Knight for one particular cargo he smuggled. He loyally served Lord Stannis Baratheon, but was not afraid to argue some of his decisions - like putting so much trust in the priestess Melisandre. This eventually led to him being imprisoned as a "traitor".
Davos was reborn, body and soul, as the captain of a Soviet nuclear submarine. Captain Zhukov's greatest adventure never made it into the history books - in 1983, his submarine the "жар-птица" (the "Firebird") was under attack from a Martian "Ice Warrior", thawed out after thousands of years in the Arctic ice. It is unknown how the Kremlin might have reacted to the way he handled the situation - especially if they ever found out he had the Time Lord known as the Doctor in his custody and let him go.
'Game Of Thrones'
'Doctor Who' - "Cold War"