It is a shame there aren't more games set in the American West. I think part of the problem is that when writers have to come up with plots for such games, they tend to fall into the habit of always going for the same type of story. Frequently its a tale of revenge, of someone's idealic, rustic life out on the open range being destroyed by outlaws or corrupt industrialists/land barons/etc. which sends the protagonist down a path to bring down the people that took everything from them and left them with nothing to lose.
Which is a shame, because the setting could lend itself to other stories as well. Keeping to a similar vein, but with a slight variation, the protagonist could be fighting to -protect- his or her family and home rather than avenge it. Red Dead Redemption did something sort of along this line and it was well received. A treasure hunt or the search for a mine could also be used for a plot, something akin to Treasure of the Sierra Madre. The setting would also lend itself well for survival horror; the people who took part in the westward expansion were traveling out into a largely unexplored and untamed wilderness, where they tried to make a life for themselves in a place where civilization and help was often at least a day's travel away. Imagine having that kind of isolation when strange, terrifying events were happening around you; finding strange tracks and other signs of abnormal things around your home in the day, and hearing unnatural, inexplicable noises at night. Do you dig in and defend your homestead? Do you pack up and run? Or the protagonist could be a new sheriff or marshal in a territory, who has to investigate strange events that have been terrorizing the settlers in the region, perhaps including some unexplained disappearances.