This is sort of prompted by the existence of
this thread on a specific service called the Islamic Bank of Bitcoin but probably deserves its own thread.
Islam, depending on how you count, is either the largest or the second-largest religion in the world, following Christianity, and indubitably the largest expanding religion in the world.
Islam has a number of interesting rules relating to money (actually somewhat resembling rules Christianity used to follow). Essentially, interest and gambling are haram (forbidden). However, the loan service in the thread I linked loans out Bitcoin, and receives payment back in the form of an identical amount of Bitcoin. This, at least on its surface, avoids the Islamic rule against interest, even though generally, Bitcoin is going to be worth a lot more when you get it back then it was when you loaned it.
This strikes me as potentially violating the rule that gambling is also haram. However, if this rule were interpreted as strictly as this, it would forbid investing in stocks, bonds, pretty much anything that might increase or decrease in value. Since many Muslims do these things, and as far as I know, no prominent cleric has denounced them, it seems this is, at least possibly, entirely consistent with Islamic law.
So, my idea, to get to it, is this. The Islamic world is one of the biggest in the world. Countries where Islam is the primary religion sometimes have exactly the kind of fiat currency problems that Bitcoin addresses. A few fatwas (simply statements from a cleric about a religious question) that Bitcoin isn't haram would really open up these markets.
As far as I can tell, the use of Bitcoin is actually entirely consistent with Islam. It's a bigger market than China.
Anyway, I'll just leave this here.
If you happen to know a prominent Islamic cleric, or know someone who knows one, consider posing this question to them and inviting a fatwa. Note: Islam is not hierarchical in structure, as such, and there is no "Pope" of Islam. Therefore, an opinion would really only be binding or even of interest to followers of that particular school.