The setting of the game should be evident, but as for guessing the exact title, hmm... good luck! (I'll provide hints as usual if needed though)

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Is it Outlaws?

A western game indeed, yet Outlaws would have been too obvious. After some reflexions, this game might not be obvious enough however, so I'll start with hints right away:

Released for a gray console, a title which includes the name of a famous outlaw.

Call of Juarez, then?

Could have been it, but no. The outlaw in question lived between 1847-1882.

Then that makes it Gunfighter: Legend of Jesse James.

Right on! Your turn now.

Alrighty, wonder how many people know this one.
Guess That Soundtrack Once Again - Putfile.com

I'm guessing it's something out of Quest For Glory... IV?

Edit: Well, I don't know for sure, but something tells me I've heard this before. Could even be from a King's Quest game. Sounds very Sierra. Or maybe I'm just being misled. :shrug:

Nope, not QFG, but you're definitely on the right track.

About time I gave another hint: 5th entry in the series.

Space Quest V then? Only SQ I have played to completion.

No, it's the witch theme from King's Quest V.

I'm skipping my turn, so whoever has a track to post, go ahead.

Yep, Rimo got it right.

Fire away:
whichisit.MID

Amayirot... argh.

NinjaguyDan's is Descent, menu theme I think? Nice one.

Edit: Next song:
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Worms World Party, right?

Worms World Party it is. Title theme by Bjørn Lynne. Your turn.

Here we go:

sendspace
putfile

That's from Azure Dreams. I played to this game a lot back in the days with my grandmother. The soundtrack as a whole was a bit repetitive, but quite memorable.

Additional Spam:
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Correct, that was from Azure Dreams which happens to be one of my all-time favorites. I'm still waiting for a proper sequel...
As for your spam, I have no idea what game that is from :)

Hint: It's from a game that could be played with the voice.

On the Dreamcast, contains "man" in the title.

It is from Seaman? My other guess was that pinball games of sorts for the Gamecube.

Does Seaman have other good music?

EDIT

I'll be gone for the next 24 hoursish, so if I'm right someone else can post the next song.

From Seaman indeed, the main theme actually.

I believe the rest of the soundtrack was rather mediocre since it's the only track I ended up keeping.