TV was still young in the early 1960s - there were only three major broadcasting companies in the country: CBS, NBC, and ABC. Looking back, an interesting characteristic of television programs at that time was a lot of focus on guns. There were shows with names like 'Gunsmoke', and 'The Rifleman'. Roy Roger's horse was called 'Trigger' and his dog, 'Bullet'. Some shows' introductions had gunfire in action or gunslingers whirling their pistols. For better or worse, we kids knew how to count out ten steps for a duel, draw our play pistols, and aim. Our training in diplomacy was minimal.

Below is a list of programs I remember from that time:

Maverick
Palladin
Wild Wild West
Rawhide
Bonanza
Wagon Train
Davy Crockett
Daniel Boone
Rifleman
Gunsmoke
The Virginian
Laramie
Roy Rogers Show - with Dale Evans
The Lone Ranger - and Tonto
Cheyenne
Branded
Wanted: Dead or Alive
Colt 45?
'F' Troop

a few that were contemporary at that time:
Dragnet
Magnum, P.I.
Get Smart
The Man from U.N.C.L.E.

and one set in the future:
Star Trek