If you like: Firefly
You might like: Defiance
Defiance is a ScyFy Channel original currently available on Amazon Prime. While it's got all the sardonic voice and grit of good westerns, it's got a dash of fantastic, sometimes light-hearted, Roddenberry-esque speculative science fiction. Several races of alien, similar and yet different to the diverse races and cultures of any average neighborhood, exist in the former city of St. Louis, now Defiance, an independent township in the terraformed American frontier.
If you like: Lost Girl, Buffy the Vampire Slayer, Supernatural
You might like: Wynona Earp
Wynona Earp, based on an IDW comic, tells the tale of Wyatt Earp's great-granddaughter, the inheritor of an old family curse and the bearer of the Colt Buntline, Wyatt's legendary weapon against the undead outlaws known as Revenants. Season One is currently available on Netflix.
If you like: Lord of the Rings
You might like: The Dark Tower
Stephen King's famous Weird West series gets pretty wild as you get further into the journey, but for a real great taste of the genre, the first four books are especially immersive. There are also graphic novels and the supplemental story, The Wind through the Keyhole, which do a great job of invoking the spirit of the genre. From what I've heard, though, The Dark Tower film is not an adequate representation.
If you like: Anything "Weird but True"
You might like: The Mojave Mysteries YouTube series
Hosted by M.L. Behrman, the Mojave Mysteries channel posts short videos between 5-10 minutes focusing on legends, tall tales, and mysteries of the Mojave desert. Exploring the real-life cross-section of desert life and the paranormal, the videos are easy-to-watch, feature some thought-provoking stories, and definitely find the flavor of the Weird West in a very real world.
If you like: Dungeon and Dragons, Cyberpunk 2020
You might like: the Deadlands Weird-West Roleplaying Game
This is the title that got me started in the genre. If you are a fan of tabletop role-playing and are looking for a new game to try, Deadlands is a rich and very immersive world with incredible detail, colorful characters and settings, lots of twists, secrets, and dark adventures. I would highly suggest finding Deadlands Revised, which has a fantastic play system after some of the bugs from the original were ironed out. There are also Deadlands Reloaded and the Savage Worlds edition.