Entities created for fraudulent purposes
Given that most people are inculcated with an unquestioning respect and obedience for governments and their symbols from an early age it is probably not surprising that certain unscrupulous individuals have sought to derive personal financial benefit from the gullible by establishing micronational entities that have a fraudulent intent.
The best known of these, the Dominion of Melchizedek (possibly named after the Biblical figure Melchizedek) was created in 1986 by a father-and-son team of confidence tricksters named Evan David Pedley and Ben David Pedley (the latter also known as David Korem) to sell fraudulent banking licenses. Melchizedek, which is supposedly an "ecclesiastical constitutional sovereignty", claims a number of territories, including Taongi Atoll, Malpelo Island, Karitane Shoal, Solkope Island, Clipperton Island and a large slab of Antarctica. Some of these are underwater, while others are territories administered by legitimate nations, amongst them France and Fiji. According to John Shockey, former special assistant, U.S. Comptroller of the Currency, in an address to the 4th International Financial Fraud Convention in London, May 27, 1999: "The Dominion of Melchizedek is a fraud, a major fraud, and not a legitimate sovereign entity. Persons associated with the Dominion of Melchizedek have been indicted and convicted of a variety of crimes."  The "government" of Melchizedek is allegedly based in the Australian capital city of Canberra, where it maintains a post office box address.
Another micronation called New Utopia, operated by an Oklahoma City longevity promoter named Prince Lazarus R. Long (born Howard Turney) - and ostensibly a libertarian new country project - was stopped by a United States federal court temporary restraining order from selling bonds and bank licenses. New Utopia has claimed for a number of years to be on the verge of commencing construction of an artificial island territory located approximately midway between Honduras and Cuba, however the selected location continues to remain resolutely submerged by the waters of the Caribbean.
The Kingdom of EnenKio, which claims Wake Atoll in the Marshall Islands has been deemed a scam for selling passports and diplomatic papers by the governments of the Marshall Islands and of the United States. 
Historical anomalies and aspirant states
A small number of micronations are founded with genuine aspirations to be sovereign states. Many are based on historical anomalies or eccentric interpretations of law, and tend to be easily confused with established states. This category includes:
These types of micronations are usually located in small (usually disputed) territorial enclaves, generate limited economic activity founded on tourism and philatelic and numismatic sales, and are at best tolerated or at worst ignored by other nations.
- Seborga, an historic principality located in the Italian region of Liguria, which traces its history back at least 1,000 years.
- Beaver Island in Lake Michigan was an unrecognized Mormon kingdom from 1848 to 1856, until its leader, James Strang, was assassinated by disgruntled followers.
- the Republic of Indian Stream, established in 1832 on territory claimed by both the US and Canada
- the Hutt River Province, a farm in Western Australia which claims to have seceded from Australia to become an independent principality with a worldwide population of 13,000.
- Sealand, a "sovereign Principality" located on a WWII-era anti-aircraft platform in the North Sea in what were international waters at the time of its foundation. These waters are now subject to claims by both Sealand and the United Kingdom. Sealand is home to HavenCo, a colocation site that advertises that customer data will be secure "against any legal action."
- Atlantium, a "global non-territorial state" claiming citizens in over sixty countries.