TOD:
Some of my favorite childhood memories are of TV westerns, including favorites "Hopalong Cassidy" and "Wild Bill Hickock" ("Hey! Wild Bill! Wait for me!" was Andy Devine's trademarked line in each and every episode...or so it seems) and "The Lone Ranger".
I, too, loved any episode of "Annie Oakley" I could watch and "The Roy Rogers Show" (Happy Trails to you...until we meet again). And there were the wonderful network TV westerns that included "Have Gun, Will Travel" (Wire Paladin. San Francisco), "Wagon Train" ("Wagons...Ho-oh!"), "Sugarfoot", "The Rebel", "The Rifleman", "Cheyenne", "Bronco", "Wanted! Dead or Alive", "Laramie" and "The Lawman."
If a show had horses and was set on a ranch, does that qualify it as a western, even if contemporary? If so, then add "Fury". And "My Friend Flicka".