I've been in 15-20 countries with heavy or dominant Muslim populations. As many have noted, the flavors of Islam are as diverse as the flavors of Christianity.
I was therefore curious to see what Islam was like in world's largest Muslim country (population 240 million, 90+ percent Muslim).
Indonesia is, of course, an archipelago in the southeast Asian tropics, so its culture and people will tend to reflect these characteristics. In addition, it has a colonial heritage (the Dutch ruled until 1949), a history as independent kingdoms, and past dominance by Hindu and Buddhist rulers.
All of these features affect people's way of practicing their religion.
From what I have seen so far (in 10 days and three cities) is a very relaxed type of Islam. People do not greet each other in Arabic ("ah salaam al'e qum" is common elsewhere; it means "peace [of the Prophet and Allah] be upon you"). The mosques tend to be small, neighborhood affairs. I do not hear the call to prayer very often, even though it's called five times per day. When I do hear it, I see plenty of people ignoring it, going about their business instead of praying.
Very few women (perhaps 10 percent) have their head covered; I've not seen any burquas ("the body bag").
In fact, it seems that most people here do not care about religion (or an outward show of religion). Unlike in other countries, nobody asks me my religion. (Many ask me where I am from.)
Addendum: I saw a lot of mosques and more religious people today on the bus, but they were still pretty chill...
All of these observations fit the profile that I had heard: Indonesian Islam is pretty relaxed.
Now some of you may recall the bombings in Bali a few years ago. Those bombings were directed at tourists, and tourists who were partying, so they seem to have been a strike against Western values (and hedonism), but I definitely think that they were the work of a tiny minority of Indonesians. Given the lax security in this country,* I am sure that there could be bombings everyday, but there probably are not because nobody wants to blow people up.
Bottom Line: Islam is not the problem; intolerance is.
Addendum (via DL): Paul Wolfowitz remembers Indonesia's ex-president as a man of tolerant Islam, but Google fears the radicals of Islam.
* When I checked in for my domestic flight, they didn't care about my water bottle (good), but there was no bag-passenger control. I could have checked in 20kg of explosives and never boarded the aircraft, and nobody would have noticed.