Laramie

From 1959 through 1963 the television western, Laramie, ran on NBC. The reruns, of course, continued for years following. They were a consistent influence in my childhood experiences of the western film genre along with Rawhide, The Big Valley, Bonanza, Gunsmoke, Have Gun Will Travel, F-Troop, The Gene Autry Show, Zane Grey Theater, Death Valley Days, Gunslinger, High Chaparral, How the West was Won, Laredo, Maverick, The Rifleman, The Roy Rogers Show, Shane, Wagon Train, Wanted: Dead or Alive, among many others.

A list of TV westerns can be found here: http://en.wikipedia.org/wiki/List_of_TV_Westerns

Wikipedia entry on Laramie:
Laramie is an American Western television series aired on NBC from 1959 to 1963. Laramie was a Revue Studios production which originally starred John Smith as Slim Sherman, Robert Fuller as Jess Harper, Hoagy Carmichael as Jonesy and Robert Crawford, Jr., as Andy Sherman. The story was about two brothers and a drifter who come together to run a stagecoach stop for the Great Central Overland Mail. The series ran for four seasons and is considered by some to be one of the best family-oriented westerns of its time.
After the first season, Hoagy Carmichael decided not to return, tired of the demands of filming a weekly episode. His character was written out with the explanation that he accompanied Andy to boarding school in St. Louis. Andy, however, would appear in a couple of episodes that second season. To restore the chemistry of the original cast, as the third season began, Spring Byington and Dennis Holmes joined the cast as Miss Daisy Cooper and Mike Williams.
When the series ended, Robert Fuller went straight to the television series Wagon Train, where he replaced lookalike Robert Horton, who'd quit the show, as the scout.

On January 1, 1962, a new version of the NBC peacock "living color" logo was introduced before that night's Laramie broadcast, and would be used before every color show on the network until 1970. Because of this, it is sometimes referred to as the "Laramie peacock".