To qualify as a western the story must take place before 1955 and include the use of horses, pistols or rifles.
The United States has produced a steady stream of western's since the 1930's; Who else is tired of hearing about how great "The Searchers" and "True Grit" are?
http://www.ranker.com/list/the-25-most-solid-western-films/guardianhps,
A Fistful of Dollars
For a Few Dollars More
Garden of Evil
High Noon
Paradise Canyon
Rainbow Valley
Red River
Rio Bravo
Shane
The Good, the Bad and the Ugly