Republic of Cuba
Who & why: the Republic of Cuba is formally inaugurated on 20 May 1902 as the US military government withdraws, and the rebel Lone Star flag of the independence wars is adopted as the official national flag. Cuba's early decades are shadowed by the Platt Amendment (repealed 1934), which reserved the US a right of intervention; the 1959 revolution led by Fidel Castro then overturns that republic's government entirely, installing a one-party socialist state that endures to this day — a sweeping change of government and ideology, but not, at any point, of flag.
What it represents: the same "Lone Star" design first drawn in 1849: three blue stripes for the island's original three military districts and two white stripes for the purity of the independence cause, a red equilateral triangle at the hoist for liberty, equality, and fraternity, and a single white five-pointed star standing for Cuban sovereignty among nations.