Religion

Religion was often used interchangeably with the terms 'faith' and 'belief system' or 'belief structure'. Broadly speaking, it was a set of stories or beliefs that were believed or gave meaning to a particular society. In many instances a certain deity or god was worshipped.

The Doctor encountered several forms of religion in the form of churches, cults, gods, deities and a variety of other forms.

Gallifrey
Religion was present on Gallifrey during the time of the Pythia when mysticism ruled Gallifrey. It was a time of psychics and prophecy. (NA: Cat's Cradle: Time's Crucible)

Later in Gallifrey's history, another 'religion' formed: a cult known as the Faction Paradox, a voodoo-organisation who revelled in the art of a paradox, something that was practically sacrilegious (if Gallifreyans believed in such thing) on Gallifrey. (EDA: Alien Bodies)

Earth
On Earth there were several instances of a variety of species masquerading within belief structures: the Gorgons controlled a sect of Christian nuns (SJA: Eye of the Gorgon); Osirians positioned themselves amongst Egyptian priests (DW: Pyramids of Mars); Exxilons visited Earth several times, influencing civilisations (and their religions) such as the Mayan and Aztec (NA: The Left-Handed Hummingbird); Cessair of Diplos was worshipped by the Druids for 4000 years (till the mid-1970s), adopting several identities while maintaining control of the religion around a stone circle comprised of several Ogri (DW: The Stones of Blood); and at least one Time Lord portrayed himself as a Christian monk while on Earth. (DW: The Time Meddler).

Divergent Universe
Within the Divergent Universe, there existed the Multihaven where a large number of religions could all exist in harmony together. While there, the Eighth Doctor and Charley Pollard claimed their religions to be 'tourists'. (BFA: Faith Stealer)

C'rizz was a member of the Church of the Foundation. (BFA: The Next Life)

Elsewhere
The Peace treaty 5.4/cup/16 specifically banned religion aboard Platform One. (DW: The End of the World)

On Delta Magna the 'Swampies' worshipped Kroll. A high priest would often dress up as Kroll to terrorise their captives. (DW: The Power of Kroll)

When the All-Gods awoke and took over the planet Dellah, religious practices became sacrosanct, and read to the letter of their beliefs; many people were punished or killed for not following a religion. (BNA: Where Angels Fear)

By the 52nd century, the Silence, the Church and the Order of the Headless were all allied to kill the Doctor to stop him reaching Trenzalore and answering a Question that must never be answered. (DW: The Impossible Astronaut, DW: A Good Man Goes to War, DW: Let's Kill Hitler, DW: Closing Time, DW: The Wedding of River Song)

Religious Iconography, Symbols and Vocations
Nuns were often associated with a particular religion; on Earth they were often associated with religions with ties to Christianity. (SJA: Eye of the Gorgon)

Study of Religion
St. Oscar's University in the 26th century had a Department of Comparative Religion, headed by Professor Urquhart. (BNA: Dry Pilgrimage) The People had an interest group called Apocalyptic Religions Interest Group. (BNA: Where Angels Fear)

The Devil
The devil idea was a form that ran through several religions. The 'horned beast' in particular was an icon that was seen on several worlds and in many civilisations. Some of this imagery could be credited to the Dæmons of Dæmos. (DW: The Dæmons)

Others could be credited to the Beast. During the 42nd century in particular several religions included The Beast within their belief structures; Arkiphets, Church of the Tin Vagabond, Orkology, Pash Pash, San Klah. (DW: The Satan Pit)