You're gonna be looking at countries with either no personal taxation (e.g. UAE and Monaco), territorial taxation (e.g. Singapore, Hong Kong), countries with tax-exemptions for foreigners that move there (e.g. Chile and Cyprus).
Here's a list:
International taxation - Wikipedia
Hong Kong and SIngapore
Territorial taxation. You can run a foreign company and not be taxed on the profits it derives outside of HK or Singapore.
Pro's:
- Highest quality of life of all the countries on the list
Con's:
- High living costs
- Must stay there 183 days a year to retain tax residency (in HK's case this changes once you have spent 7 years there - at that point you have a lot more freedom)
Cyprus
No personal tax on dividends for foreigners that become residents. You can run a foreign company (or even a Cyprus company) and pay yourself solely in dividends, paying 0% personal tax.
Cyprus recently enacted CFC rules for companies (2019) but have no CFC rules for individuals yet. This means that you can run your foreign company while staying in Cyprus, without having the company be considered a tax resident of Cyprus, and without paying the 12.5% corporate tax of Cyprus.
Pro's:
- The residency is very accessible to EU citizens
- It is cheap to live there compared to Hong Kong and Singapore (except for Limassol, rent is beteeen 25-50% of HK and Singapore)
- Using their 60 day rule you can stay there for 60 days a year only (Note: This costs $10k in annual expenses to maintain)
Con's:
- Not the same quality of life as in HK or Singapore
- They are currently introducing an exit tax
For a cheaper alternative to the ones above, you might go to Chile (0% personal tax first 6 years), or any of the following territorial taxation countries:
Georgia, Panama, Costa Rica and Paraguay.
The quality of life will be lower in those (compared to HK, Singapore and even Cyprus).
Other honorable mentions
If you have a decent income of about $50k or more a year, you may also consider Andorra. They have a 90-day rule, which lets you stay there 90 days only, while still maintaining residency.
Gibraltar, Monaco and certain Swiss cantons are also options, if you are loaded with cash.
Another option is Croatia. Croatia does not have CFC rules for individuals. You can run a foreign company without it being considered tax resident of Croatia. Personal income tax is 12%. Possibly has higher quality of life than Cyprus. And is much cheaper than HK/Singapore.
If you're okay with paying some tax, Hungary might also be an option. However, you cannot run a foreign company there due to the CFC rules. Same for Romania and Bulgaria.
Giving up your citizenship
Lastly, there is the option of giving up your citizenship and buying a citizenship of a Carribean island (e.g. Nevis). This is the only real option for US citizens.