Leaving aside the developing and underdeveloped nations discussed in the article, the two cheapest right now look to be: the US ($500k equity in a job creating business for four years) and Portugal (€500k in real estate for five years).

The big disadvantage to the US program is that it has fairly strict residency requirements and, almost alone, taxes on worldwide income. Portugal appears to have much looser residency requirements (both to maintain the visa and to ultimately apply for citizen) but I'm far less familiar with its program and could be missing some nuance.

Hungary's program is €300k (in special government bonds), but I don't think they are considered a developed nation yet. (they used to be called 2nd world, but that category seems to have dropped out in the new developed/developing/underdeveloped scheme).

Speaking from my home in Budapest, I can tell you with utter confidence that if you don't consider Hungary a developed nation you need to do a little more research.

Hungarian citizenship lets you live and work anywhere in the EU, which is attractive even if you don't want to live in Hungary.

Kind of like how being born in Wyoming gives you US citizenship, which lets you live and work anywhere in America, even if you wouldn't want to live in Wyoming.

Right, but as I understand the rules, in order to get citizenship you need significant Hungarian residency over the course of several years.

So? There are no passport checks in EU. You can get a residency in Hungary, and live somewhere else in the EU.

If we are going to include fruad there are lots of things you could do.

Not necessarily fraudulent, I think there are some EU rules that permanent residents of one country can live and work in other countries. I don't know the specifics though.

Spain and Ireland also have programs where you can buy houses, gain residency (but not work permits), and then become a citizen after 5 years.

I've been living in Ireland for 2.5 years and was really excited to become a citizen, but am returning to the US for family reasons, which is bittersweet. My time spent here still counts towards the residency calculation, should I return in the next four years.

In what sense do you consider Hungary not to be a developed country?

As I tried to indicate the current classifications are a bit of mess. You can see the different definitions in use by various entities in this wikipedia article: http://en.wikipedia.org/wiki/Developed_country