Definitely the biggest cultural change for me so far is simply living in a nation that is 97% Muslim. In the US, we talk about separation of church and state, and a lot of times we whine that they aren't separate enough (a la "In God We Trust" on our dollar bill or having the 10 Commandments in a courthouse). Next time someone complains that we as a nation are "too religious," I recommend they come visit a Muslim country. Here, religion is intertwined into every aspect of life; from the phrases you use in every single conversation, to the way you can or cannot dress, to how much you're allowed work during holidays, to the amount of time you can spend with someone of the opposite gender, to when and where you can eat and drink, and the list goes on and on.
The most obvious way that Islam is visible for me is the Adhan, or "call to prayer." Five times a day, Adhan is called out by the holy leader from the mosques over loud speakers. This signals to everyone that it is time for the Muslim's prayers. Its essentially a chant that lasts for about 3 minutes, and there is no place in Amman that this cannot be heard. The reason that it is projected from the mosques so that everyone in the city can hear it (according to wikipedia) is: "to make available to everyone an easily intelligible summary of Islamic belief. It is intended to bring to the mind of every believer and non-believer the substance of Islamic beliefs, or its spiritual ideology." It is essentially a three minute summary of Islamic doctrine, five times a day; and while in the States we might think that this is invasive, offensive, or annoying, I have developed a deep appreciation for this incredibly beautiful chant.
Every time the chant begins, I stop and listen (with the exception of the one that happens every day at 4:15am... then I just wake up really grumpy and wait for it to end). It is so moving, and even though I don't agree with the theology, it is a great reminder of how I should be spending my time and who I should be serving. Five times every day, I use these three minutes to reflect, be still, release my frustrations, and re-set my attitude. I've found that repurposing the Adhan and taking some quiet time has been one of the most helpful things I've done to help cope with the constant stress of living in a radically different culture.
Here is a recording of the Adhan (the first 10 seconds are silent, but it comes on after that). Now imagine this call echoing over the seven hills that make up Amman. It truly is beautiful.