Does anyone here know any good games (or mods for games!) set in that time period?
I don't mean simulations or strategy games or something like that, I mean games with a main character that you control, who has his/her own story.

To be perfectly blunt: I want Vampire: The Masquerade Bloodlines, only set in somewhere between 1900 and 1920, roughly. Just so you can imagine what type of game I'm thinking of: Not a huge open world or anything, just a small but detailed and atmospheric world that lets you relive that period of time.
I have looked and looked, but I can't seem to find anything that comes close. And I can't believe that - this time period has so much to offer and is so nice to look at, surely some game company has used it as a setting?!

I don't know about any games in that exact period. The best I can do is L.A Noire, The Godfather / II, Mafia / II. They're all in the 40s.

The only game I can think of right now in that time period is Red Dead Redemption, but I'm pretty sure that it's not the type of game your looking for. It's more like GTA than Bloodlines.

Like GTA is fine, the problem is that there are veeery few games that are like GTA and I know all of them, I believe.

I originally wrote a long introduction to this thread in which I complained how nearly every time period EXCEPT this one is already covered by some awesome games. Like, from the 30s on we have great games centered around mafia or organized crime stuff, and of course for the 90s and later we have dozens of great games, one being Vampire Bloodlines. For the Wild West we have Red Dead Redemption, Call of Juarez, Desperados...
But not a single game so far lets me take the steam train to Prague and drink a coffee with Franz Kafka.

Wait for Bioshock Infinite next March, it is set around 1915.

Seems he's looking for something a little more realistic, otherwise I'd have recommended Shin Megami Tensei: Devil Summoner games by now.

Call of Cthulhu: Dark Corners of the Earth?

Yes, and it will be awesome. But, you know, Bioshock is completely crazy. It's a wild fantasy setting where everything is completely over-the-top. There's nothing wrong with that, mind you, I'm really looking forward to that game, but mostly not because it's a period piece.

Thanks for all the suggestions so far though, I appreciate it.

I actually just came across the Sherlock Holmes games, and apparently some of them are half-decent, and they look pretty good. It's not exactly the right time period and the focus on crime-solving is not really what I'm looking for, but in case anyone else is interested - apparently "Sherlock Holmes vs Arsene Lupin" is the best one and it features a sort-of-open world (that is, much more open than is usual for adventure games).

Call of Cthulhu: Dark Corners of the Earth is set in 1915. It's pretty awesome. It's a horror FPS and you play as a detective.

Aside from all the Lovecraftian stuff obviously, the setting is pretty realistic.

http://www.youtube.com/watch?v=DbfLvboZBrU

Oh wow, what an atmosphere! That game looks really excellent. I just hope it won't be too intense for me.
Thank you very much for this recommendation.

I can't believe noone has said this yet.

Red Dead Redemption
Set in the early 20th century, 1911 i think it is.

red dead redemption's set in 1901 i believe
scratch that been beat to the punch