With regard to economic freedom, you'd want to take a look at small Asian countries and Free Economic Zones, such as Singapore, Hong Kong or Shenzhen. Recently a new Free Economic Zone popped up in Honduras, so that is something I will keep an eye on as well.

But the countries that offer the most libertarian lifestyle, in my opinion, are some European countries:

• Switzerland: Divided into 20 cantons and 6 half cantons (these are like separate states) that have their own constitutions. Culturally, the country is divided into 4 languages: Swiss German, French, Italian and Reto-Roman.
  
  These cantons compete for residents, which tends to drive down income taxes. The country is doing well economically too. Guns laws are also relatively loose in Switzerland.
• Liechtenstein: Very small country with only 37,000 residents. 40% of all residents is foreign and immigration laws are fairly loose. The basic income tax rate is only 1.2%, but the different communes add around 15% too, which is still very low compared to many countries.
  The constitution of Liechtenstein gives the communes a right to secede from the principality. The country has no army and chooses to remain neutral in any conflict. Crime is also very low and sometimes they don't even have prisoners.
• Andorra: A very small country in the Pyrenees mountais, in between France and Spain. The country used to do very well economically with a business tax of only 10%, but they had to raise taxes due to pressure from other EU member states. So I think this one is losing the fight against big government, sadly.

If you're looking at Latin America, I believe Chile is the freest country. Gun laws are relatively loose and in the country side you can live pretty freely in some places.

If I have missed other countries, let me know! I hope my comment helps.

Source of the image

EDIT: Iceland also has relatively loose gun laws and they jail bankers, so that's pretty cool. ;-)