The seeds for the long-lasting character of Brigadier Lethbridge-Stewart were sown in the Troughton era. Lethbridge-Stewart, then a Colonel, appears in "The Web of Fear" as a standard military figure, in charge of a platoon of men assigned to maintain a fortress near the Goodge Street Underground station, with the premise that London had been evacuated and that the military had been put in charge of regaining control of the Underground.
The idea began to grow in "The Invasion," an earthbound story with the Cybermen in which UNIT makes its first appearance. Derrick Sherwin and Peter Bryant, who were co-producing Doctor Who at the time, wanted to lay the groundwork for making Doctor Who earthbound for a time. So they introduced UNIT with the previously-existing character of the Lethbridge-Stewart, now promoted to Brigadier, as its head.
The Brig came into his own with the beginning of the Pertwee era, which could also be considered the beginning of the UNIT era: stories in which the earth is threatened either by mad scientists at home or aliens bent on takeover. All are defeated, of course, by a combination of the Doctor's ingenuity and UNIT's firepower.
The Brigadier and UNIT continued to have a significant presence through seven seasons, finally fading away with "Terror of the Zygons," "The Android Invasion," and "The Seeds of Doom." Sadly, the era ended not with a bang but with a whimper, with the Brigadier not even appearing in the latter two stories.
The Brigadier is a stolid, straightforward, by-the-book fellow: someone you'd definitely want to have on your side when facing any straightforward menace. Certainly one of his sterling qualities is his willingness to be on the front lines and not order his men to do anything he wouldn't do himself. Though he had trouble grasping the nature of the assorted menaces UNIT and the Doctor had to face, he always retained his composure and was prepared to assist the Doctor as best he could.
What makes the Brig a truly classic character, however, is his return appearances. In "Mawdryn Undead" he has left UNIT and is now a schoolteacher. (Curiously, the part was originally considered for either Harry Sullivan or Ian Chesterton and only rewritten for the Brigadier when it was found that Nick Courtney was the only actor available.) In "The Five Doctors" he is handing the baton over to Colonel Crichton when he and the Second Doctor are whisked off to the Death Zone on Gallifrey. In "Battlefield," he gets back in the saddle again, helping the Doctor ward off Morgaine and the evils she has brought to earth.
With "Battlefield," Nick Courtney had worked with six of the seven Doctors. This deficiency was remedied in "Dimensions in Time," in which the Brigadier, complete with helicopter, gets to work with the sixth Doctor. It's also worth mentioning the radio programmes "The Paradise of Death" and "The Ghosts of N-Space," which to some extent revive the UNIT days with the Third Doctor and Sarah Jane Smith.
Somehow I think we have not seen the last of the Brigadier.