"Vigilance is our shield that protects us from the squalid past. Knowledge is our weapon with which we carve our path to an enlightened future" (Hammerite Chant).
The Hammerites (or "Hammers") are a religious group in the Thief universe which centers around the idea of a god named "the Master Builder." It is the belief of the Hammerites that the Master Builder gave mankind tools-the hammer, the nail, the beam, etc.-in order that man might build structures and rise out of the chaos of nature. With such a belief, the Hammerites stand in direct contrast to the Pagans, who live in the wilderness and worship a pantheon of gods, of whom the most important is the Trickster.
As construction is such a central tenent for the Hammerites, they not only serve as the religious insititution of the City but also drive technological progress in the City ("the City" being the setting of the Thief games). This connection between religion and technology is most apparent in Thief II: The Metal Age, when the religious group known as the Mechanists leads the City into an industrial era.
In Thief: The Dark Project, the Hammerites, though a powerful religious institution, seem to have declined in power. Though they run Cragscleft prison and so have the power to send criminals there (and so play some kind of a role in government), they themselves are not the government. It is apparent from a conversation between two guards at the entrance to Lord Ramirez's estate (in Mission 4 of Thief: The Dark Project) that the Hammerites used to be the absolute power in the City, but that at a certain point the government became secular and the Hammerites became only one of many players in power.
In Thief II: The Metal Age, the Hammerites became obscure and almost forgotten as the City moved towards the Mechanists, a religious group that splintered off from the Hammerites and who the Hammerites considered to be heretical. The Hammerites objected to certain tools that the Mechanists believed should be used in construction; the Hammerites thought that the Mechanists were twisting the scripture of the Master Builder. As the Mechanist Order falls after the events of Thief II, the Hammerites return to being the primary religious institution in Thief: Deadly Shadows.