Torchwood stun guns worked by "shocking" targets in physical contact with the muzzle in a manner similar to a taser. They had two settings; one for killing and one for stunning.
The team used stun guns to capture Max Tresilian, who was rampaging in a bar. (TV: They Keep Killing Suzie)
Gwen Cooper used a stun gun against her boyfriend Rhys so she could take him to the Hub without having to convince him to go. (TV: End of Days)
The team used the stun guns when investigating the factory exploiting the Cash Cow. (TV: Meat)
Ianto used one on Billy Davies, a hit man working for the Pharm. (TV: Reset)
Gwen Cooper used one to stun Jack in order to drive him away and trade him for her family. (TV: Immortal Sins)
On one occasion, Jack Harkness accidentally killed a Histrix when he thought the gun was set to stun. (AUDIO: Asylum)