Panama
Part of the reason Panama was able to gain independence in 1901 was due to American interest in building the Panama Canal, and relations have been generally strong since then, with 25,000 U.S. citizens living in Panama and a mutual healthcare program.
Georgia
The U.S. established strong diplomatic relations with Georgia after its independence from the USSR in 1991; since that time, the two nations have cooperated on trade and security. Relations are so strong between these countries that tourists can actually stay in Georgia without a visa for up to a year.