Is there a list of these countries somewhere? The only country that I know of that sells citizenship was Sealand (they don't anymore, but they were offering passports as a fundraiser).

http://principality-of-sealand.eu/faq_e.html

Actually, the above website may not be from the REAL Sealand... long story.

At the moment there's only two countries left that formally and openly grant citizenship with zero years of required residency in exchange for cash: St. Kitts and the Commonwealth of Dominica. In the 1990s there were a lot more (Grenada, Belize, Marshall Islands, etc.). Montenegro used to do this too up until recently but they came under pressure from other European countries to stop. Austria is rumoured to do it under their "contributions to national interests clause" (the one that other countries usually use to naturalise soccer players) but the price tag is in the 7 or 8 US$ figure range.

http://ciu.gov.kn/

http://www.dominica.gov.dm/cms/index.php?q=node/678

https://www.henleyglobal.com/countries/austria/citizenship/

On the other hand, dozens of countries will give you a visa in exchange for an investment; there's nothing unusual about the US in that regard, contra what forgottenpasswrd tries to imply. In some cases the "investment" is just a purchase of government bonds; in other cases it means an actual business that is capital-intensive and generates good jobs for locals. After you get the visa, you still have to actually live there for some period of time and show evidence of integration (like speaking the language) to qualify for naturalisation. The amount of money and the period of time range from four or five figures and a couple of years (Peru, Ecuador, Paraguay, Dominican Republic) all the way up to seven figures and the better part of a decade (Hong Kong, Germany).