Game designers are at a disadvantage with alternate histories as they are usually developed fromthe perspective of a limited audience. If I was to seriously consider a alt-history background I would look at the forums at http://www.alternatehistory.com/discussion/ maybe submit it to be criticized.
Subjects like the South winning the civil war and Germany launching Sea Lion have been discussed so many times that you really learn what the possibilities were.
The most interesting timelines written are those that start from an otherwise uninteresting Point of Departure. For example Jared's Decades of Darkness has a PoD of the death of Thomas Jefferson in late 1808. This change leads to an extended Embargo Act, leading a more widespread succession movement in New England, A war of 1811 where New England along with New York and New Jersey leaves the Union, the resulting Union is dominated by slave holding states, which leads a slaving holding, debt peons dark United States in the 20th century that is powerful nation dominating the Americas yet is a pariah among the rest of the world. http://decadesofdarkness.alternatehistory.com/
The way these timelines work is that you start out with a short story or a series of vignettes, people comment on them, you modify any implausibilities, and then post the next step. If you take this seriously the result is a plausible timeline that been vetted by many eyeballs. Avoiding the pitfalls that plague backgrounds of this kind.
For example you would do something like
What if while in his early teens Mohammad converted to Christianity and stayed in Syria living as a Monk. Then you post a series of vignettes about Mohammad as a Christian monk. Perhaps your initial plot is that Mohammad instills a missionary zeal/conversion by the sword attitude in Byzantine Christianity as result of his experience in the wars with the Sassanids. (they held Syria and the Holy Lands in the 620s) This in combination with Heraclius as Emperor led to the Eastern Roman Empire recovering before the Sassanids.With eventually leds to a Roman Empire that survives into the present era dominating Europe. Along the way Steam came into early widespread use because of the increased traffic resulting from a stable eastern empire. This ignited an early industrial revolution somewhere in the 16th to 17th century. Some tech is more advanced (metallurgy, steam, coal, etc) while other are still at OTL (Our Time Line) levels.
You could use this as a background for some weird steampunk RPG. By working it out first with outside input you can create a plausible chain of events to get to your "present." The plausibility helps to allow your audience to accept the background as part of the setting.
The techniques that the alternate history folks use help with standard backgrounds for fantasy and science fiction games as well. You start with a initial set of premises and work your way to your setting's present making sure each step is plausible. This helps with game balance with extranormal rules systems like magic and psionics. You can spot elements that have undesired effect and fix it before releasing the system. For example having a Create Metal spell has a radical effect on fantasy societies and probably would make medieval/feudal societies implausible. You could eliminate the spell or fix by saying the metal being created doesn't last for then the spellcaster's level in days.