In 2005 a movie was released that changed pop culture in a big way and Wyoming was the center of it all.  Brokeback Mountain is the best movie set in Wyoming, according to Thrillist.

Some of you may already know that Brokeback Mountain was not actually filmed in Wyoming, it was filmed in Canada due to budget costs.  But the film is set in the Wyoming mountains with two male sheepherders who fall in love essentially.  The two sheepherders were played by Heath Ledger and Jake Gyllenhaal, who both received Oscar nominations for their more intimate scenes.

The film received great reviews, Rotten Tomatoes gave it an 87% and IMDb gave it 7.7 out of 10.  It ended up bringing in $178,062,759 worldwide in the box office.