The Republic of Minerva is probably one of the most famous micronations in the entire world. The country was formed in 1972 by Michael Oliver, a millionaire who made his fortune in real estate. The country had no taxes and no government interfering in social issues.
The Dominion of Melchizedek is considered one of the most extreme cases of micronations. The nation was formed in 1986 by Evan David Pedly and Mark Logan Pedley, both of whom served time in prison. The island issues passports for $10,000 apiece.