My favorite western is Once Upon A Time in the West. Anything made by Sergio Leone is an instant classic. I also really like the old John Ford westerns, even the black and white ones. The Man Who Shot Liberty Valence is probably my favorite Ford western, because it's the only time John Wayne plays a character who suffers an existential crisis, and he has to play second fiddle to Jimmy Stewart. Winchester '76 is another great black and white western that Jimmy Stewart stars in. He's known by most folks for being in It's a Wonderful Life and Mister Smith Goes to Washington, but he had extensive work in westerns. The Shootist is another good one that Wayne and Stewart share screen time in, and it's especially poignant since Wayne plays a character dying of cancer, while he himself was suffering from cancer. I think it was his last film if I'm not mistaken.
Too many people discredit entire generations of films just because they're black and white, and I believe this is a huge mistake. The Hustler, Out of the Past, A Touch of Evil, Sunset Boulevard, 12 Angry Men, Anatomy of a Murder, On the Waterfront, and many, many others are all classic "noir" films that outshine almost anything made today. Granted, they made a whole lot of crap back then, too, but time is the best filter for quality. I'd rather watch a good old movie than virtually anything contemporary, save films made by a select few, such as the Coen Brothers.
One genre that's harder to get into is classic Jedaigeki. I've seen Kurosawa's samurai classics like Seven Samurai, Yojimbo, Sanjuro, Roshomon, Spider Skull Castle, Kegemusha, and Ran, and it leaves me thirsting for more slow paced, expertly photographed, and infinitely fascination feudal Japanese action. Hanzo the Razor is an interesting series that seems to borrow heavily from blacksploitation cinema from America, as evidence of its jazz fusion soundtrack and the protagonist's infamously enormous manhood. I intend to look into some of the Zatoichi films, but there's so many it's hard to figure out where to start. And then there's acquiring the films to begin with-- they don't sell that shit at the Redbox.