Which other country/region is the most different from America?

[Franknburger]

To answer that question, one must first define America. A few things that come to my mind:

1.) Diverse (ethnically, geographically, various subcultures): That criteria would exclude countries like Nigeria, Ethiopia, Indonesia, China, India, Russia, South Africa, even Afghanistan, Irak, Iran and the Sudan, that also display a considerable degree of diversity.

2.) Second world: Immigrant tradition, pioneer spirit, high mobility, comparable low respect for local traditions and heritage (though that seems to be gradually changing): Obviously puts most other second-world countries, i.e. Latin America (with the possible exceptions of Bolivia, Ecuador and Guatemala), Australia and New Zealand, off the list.

3.) Urbanised and industrialised: Pretty self-explaining. Takes out most of Europe and East Asia (probably even North Korea).

4.) Democratic, individualistic, protection of the individual's rights: If there were any European countries left that not already would be excluded by the "Urbanised & Industrialised" criteria (the Faroe Islands come to mind), they are out now.

5.) Strong religious (Christian) roots: If you look at the Christian part, you would get many Muslim countries as obvious antagonists. When you, however, consider the overall influence of religion on policy and individual behaviour, I see quite many parallels between the US and the Middle East.

6.) Anglophone: Speaking the same language facilitates the transmission of culture and values, so the most 'un-American' country is most likely not Anglophone. Here goes a lot of sub-Saharan Africa, including Somalia (or at least Puntland, its northern part).

What does that leave us with?
a.) Francophone Africa, especially Sahel countries like Niger and Chad. Quite a good fit, if it weren't for their ethnic diversity .. The same applies to Indochina (Laos, Cambodia).

b.) Various island states: Papua-New Guinea is Anglophone, quite close to Australia, and extremely diverse. Except for not being Anglophone, the same applies to East Timor. Greenland is too similar to Alaska to qualify. French Polynesia has been heavily exposed to American culture during and after WW II. Madagascar is pretty diverse, and has been settled simultaneously from the African continent, the Arab peninsula and the Malayan archipelago. Tourism hotspots (Maledives, Seychelles, Mauritius) can be excluded as well. That leaves us with Sao Tomé & Principe, which, however, is quite urbanised (62%).

c:) Inner Asia: Kazakhstan, Uzbekistan, Afghanistan and Nepal are too diverse (Uzbekistan is also serving as US supply corridor to Afghanistan). Mongolia is quite urbanised (62%). Kirgizstan had sizeable German-Mennonite settlement since the early 19th century, which should have left cultural traces similar to those that can be found across the US Midwest. So the choice is down to Turkmenistan, Tajikistan and Bhutan.
Tajikistan: Haven't been there, but to Northern Afghanistan close to the Tajik border. As a Persian (=Indo-European)-speaking country that was part of Alexander the Great's realm, it should be more "European", and as such also "American", than one would initially assume. Still very different from the US, but not enough to make it to the top of the list.
In terms of political culture, Turkmenistan is an obvious antagonist. However, its oil-based economy implies strong economic interaction with the US, and the development vision is quite "American".
Bhutan is a Buddhist state. While one may say the influence of religion on politics makes it somehow American, the differences between Christianity and Buddhism are so pronounced (much stronger than the differences between Christianity and Islam) that I tend to see it as the culturally most un-American country in the world.

BTW: From a "Let's explore some unknown territory"  perspective, Antarctica (as the Moon and Mars) is as American as it can get ...

[Franknburger]

I don't think a country being diverse would necessarily make it too similar, and prevent it from being  very different from the USA. Both Papua New Guinea and India are very diverse... but they're even more diverse than America is, and the diverse cultures in those countries are extremely different from the main cultures in the USA.

When putting down my full post, I already realised that I had not fully thought through the diversity point. Essentially, diversity has a number of socio-cultural implications. Federalist and autonomist tendencies are one of them. But diversity also works on values & behaviour, in quite different ways that may range from accepting (maybe even expecting) other people being different from you in attitudes and behaviour, towards formal and informal mechanisms of segregation, up to open racism. 
As such, I agree that while diversity favours certain patterns that are found in America, it does not necessarily have to make a country similar to the US. This applies especially to countries in which a good part of the diversity exists in isolation from each other (e.g. Papua New Guinea).
Having said that, a quite typical feature of diversity is that it promotes ethnically / religiously segregated housing, which you find across the US as well as in, e.g., most West African countries, or in Irak.

Also, is the Francophone world really that different from the Anglophone world?

All non-Anglophone countries (unless there is a sizeable number of US troops or tourists there)  are certainly less exposed to American media and culture than Anglophone ones, which makes them more likely of being "non-American".
Also, my experience as someone who is using both English and French as foreign languages is that English communication is quite straight-forward and business oriented, while French tends to be more polite and subtle. In general, language determines your expression, thus strongly influencing your way of thinking, and shaping the culture.

As for the Germans in Kyrgyzstan, they make up less than 0.3% of the population.

Today, yes, since most of them have re-migrated to Germany. However, in the 1970 USSR census, their share was still 3%.

[Franknburger]

To answer that question, one must first define America. A few things that come to my mind:

2.) Second world: Immigrant tradition, pioneer spirit, high mobility, comparable low respect for local traditions and heritage (though that seems to be gradually changing): Obviously puts most other second-world countries, i.e. Latin America (with the possible exceptions of Bolivia, Ecuador and Guatemala), Australia and New Zealand, off the list.

Seriously?

Yes - though the correct term that I was thinking about is "New World", not "Second World". But there are substantial cultural differences between the Old World and the new World. The whole fracking stuff, for example, is a no-go in most of Europe, where you will find a medieval church every 10-20 miles.  The following links might give you a better idea of what I mean:
http://en.wikipedia.org/wiki/Staufen_im_Breisgau
http://www.swissinfo.ch/eng/business/Geothermal_sector_faces_heat_of_public_scrutiny.html?cid=8022548
http://www.renewableenergyworld.com/rea/news/article/2013/04/france-geothermal-energy-debate-when-is-fracking-not-fracking

Note: Please look at the links from a cultural perspective. Any technical discussion would IMO be better placed in a separate thread.

[Franknburger]

I have come across the World Values Survey that tries to answer the question in an empirical way. Based on survey launched every five years, they organise countries in a 2-dimensional matrix:

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This is the resulting map for 1999-2004:


Some of their placements run counter intuition (compare e.g. Austria's position vis-à-vis Great Britain and Germany). I also tend to think that the survival / self-expression scale may rather capture a country's current situation than underlying cultural values, as changes by half a point or more from one cycle to the next are quite common. [Questions here include neighbourhood security & pollution, environmental taxation, "maintaining order" vs. "free speech", confidence in the police, the parliament, and government, etc.). Moreover, I don't think that "party membership" is an adequate measurement to conclude on survival / self-expression values when comparing between the US, Western Europe, post-communist countries and China.  The fact that more than a third of respondents in Germany and Japan never use a computer raises some doubts on representativeness.

Nevertheless, here is their latest 2005-2008 map (next update will come in 2014):



So, what is their result on which countries were most different from America in 2008 (sum of absolute differences on both scales)?

1. Taiwan (4.91)
2. Hong Kong (4.75)
3. Bulgaria (4.71)
4. Japan (4.58)
5. South Korea (4.56)

In 2004, the Top 5 were Russia, Bulgaria, Ukraine, Estonia and Moldova.

Oh, and the closest one in both 2008 and 2004 - surprise, surprise: Canada.