GUN

Not great, but I had a lot of fun with it.

Westerado(not related to Desperados)
Freddy Pharkas
Super Amazing Wagon Adventure(absent here)
West of Loathing

I'd love a PC port of Cowboys of Moo Mesa or Sunset Riders.

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I enjoyed it too, it's worth a playthrough. Up until Red Dead Redemption was released, Gun was the best Wild West open-world game we had.

@OP : Yes, Desperados : Wanted Dead is a fantastic game, the sequels are nowhere as good as the first game, but still quite enjoyable if you liked the first.

Aside from those already mentioned (and the sequels to Desperados, which Helldorado apparently is one of), there's also Oddworld: Stranger's Wrath, which is a first-person/third-person shooter with platforming elements. Not set in the "Old West" per se (it's an Oddworld game), but it's still basically a Western.

Similar deal with Rebel Galaxy: arcade-style spaceship combat game, kinda like Firefly with alien races thrown into the mix. Honestly, though, without the dirty country-blues soundtrack, I'm not sure I would even consider this Western-like, so YMMV. (Full disclosure: this is the only one of these I've played.)

There's also A Fistful of Gun, which is Western-themed more-or-less-top-down shooter. It looks kinda "busy" to me, but if you're into shoot-em-ups....

Not on GOG, but I would be remiss if I didn't mention Rockstar's Red Dead games (Revolver and Redemption, as well as the latter's Undead Nightmare expansion). I know that Red Dead Redemption is often considered about the best video-game Western of all time (not that there are that many to choose from). But again: haven't played it. EDIT: Also, I think Redemption's supposed to get a sequel this year.

Is Red Dead a console only?

left field very good game with western feeling: Rimworld

Yes, though progress is being made on the PS3 emulator with RDR running in 4k, I heard even last year it wouldn't run at all so they seem to be on the right track

It's a console-exclusive unfortunately. If I understand it correctly, the engine/code they used is a real mess, a PC port would be extremely difficult from a technical standpoint, it's highly unlikely we'll ever see it on PC. The PS3 emulator is coming along pretty nicely, so there's that. Well, at least the highly anticipated sequel will release on PC.

Yes, you must register with Rockstar Club and run it through Steam with a dash of Denuvo, makes me wanna throw up really

May want to skim this recent thread:

https://www.gog.com/forum/general/wild_west_games_with_playable_women/page1

While the poster is looking for a specific topic, the genre is discussed a bit.

Hope this helps