- Torchwood One, the main headquarters, was in London. It featured in "Army of Ghosts"/"Doomsday" & was destroyed in that story.
- Torchwood Two was in Glasgow & seemingly consisted of one person, whom Jack (of all people!) described as "A very strange man."
- Torchwood Three was in Cardiff. That branch is the one featured in the Torchwood series. Since the events of "Children of Earth", Torchwood Three has effectively been defunct, though Jack & Gwen survive.
- Jack said, "Torchwood Four's kinda gone missing, but we'll find it one day." So far (May 2015), there's no sign that Torchwood Four has been found -- by anyone. No location was given for this branch.
In addition to these, a Torchwood India has been mentioned in audios & novels as having existed until 1924.
Since the Torchwood Institute was set up to protect the British Empire, not just Britain herself, & that empire once covered a quarter of the planet's land surface, there may have been other branches that have not so far been mentioned individually.