Trigun is the standard answer for this. Another of the same author's (Nightow) work is Gungrave which is similar but more of a modern crime/mafia setting. Cowboy Bebop lives up to its name in this respect as well.

A classic show City Hunter (originally made in the 80s, but survived in many forms over the years) has strong elements of a western-cowboy style. Probably best described as an anime version of Miami Vice.

You might also look into the Captain Harlock and related series. Some of those are distinctively western-themed.

Trigun is the standard answer for this. Another of the same author's (Nightow) work is Gungrave which is similar but more of a modern crime/mafia setting. Cowboy Bebop lives up to its name in this respect as well.

A classic show City Hunter (originally made in the 80s, but survived in many forms over the years) has strong elements of a western-cowboy style. Probably best described as an anime version of Miami Vice.