Perhaps most of you think the answer is Vatican City. It's just a bunch of churches in the middle of Rome, right? Well, not quite. The smallest, recognized sovereign state in the World is the Knights Order of Saint John or the Knights Hospitaller as it is known in pop culture.
What's the span of this country? Well, here's the quote from Wikipedia
With its unique history and unusual present circumstances, the exact status of the Order in international law has been the subject of debate. It describes itself as a "sovereign subject of international law." Its two headquarters in Rome — the Palazzo Malta in Via di Condotti 68, where the Grand Master resides and Government Bodies meet, and the Villa Malta on the Aventine, which hosts the Grand Priory of Rome — Fort Saint Angelo on the island of Malta, the Embassy of the Order to Holy See and the Embassy of the Order to Italy have all been granted extraterritoriality.
So... two headquarters, a fort, and two embassies.
And yes, they're recognized fully by more than 100 countries and the UN. The reason why some might not consider it a country is because they lack territory. But you see, thanks to history, they retain their sovereignty even though they have no territory.
So you may ask the question, why? The Teutonic Order didn't retain their sovereignty when they lost territory so why did the Knights of St. John did? Well here's the difference: The Teutonic Order's Grand Master, converted to Lutheranism and swore fealty to Poland, effectively making himself Duke of Prussia and this forced the Teutonic Order to return to its overlord, which is the Holy Roman Empire. Eventually, the Emperor began to appoint second sons to be Grand Masters of the Order effectively ending the sovereignty because the Order became subject of Austria.
The Knights of St. John on the other hand, only got the territories they held conquered by outside powers. First, they got Rhodes conquered by the Ottomans. After seven years without territory, they were granted Malta by Charles V, Holy Roman Emperor, Archduke of Austria, King of Spain, Hungary, Sicily, the Other Sicily, and... you know what, here's what he got
So yeah, Malta is nothing when compared to all of that.
Anyway, Napoleon had to reign on their parade and took Malta off of them in 1798. Unlike the Teutonic Order however, they were not annexed by Napoleon, only occupied. Under the treaty of Amiens in 1802, France 'returned' Malta to the Order but since Britain already annexed Malta, the Order couldn't return to Malta.
Later on in 1834, they bought two offices in Rome and they finally had 'territory' again. Albeit small, they managed to retain sovereignty in the 32 years without territory. So, how could a nation without territory retain sovereignty? Recognition of course. Hard to argue when the big boys say you're a country, right?
So some statistics from Wikipedia: The Order has a whopping 3 citizens and has been independent since 1099. Sealand in comparison, is claimed to have 27 which is 9 times more than the Order. The Demonym is Hospitaller or Malteser and official language is Italian. This means that only three people in the World can legally claim 'Hospitaller' as their actual nationality.
Sovereign Military Order of Malta passport
For now, the Order has no naturalization policy nor residency so you can't apply to be a Hospitaller. You can however, become a member. Contact the Grand Priories or National Associations and submit your proposals there (list here: http://www.orderofmalta.int/the-order-and-its-institutions/28198/national-institutions/?lang=en ). It's likely you'll have to be Catholic though or have to convert to it.