In 2014, in an unclaimed patch of land between Serbia and Croatia, a savvy Czech politician created The World's Newest Country (maybe). But honestly he seems to be doing everything right and following proper international law, and both Serbia and Croatia said the land is not theirs, so there is an actual chance something interesting will happen.

Back in 1967 an astute Brit occupied an abandoned fortress built in international waters during World War 2 - and it remains in continuous occupation since then, unchallenged in it's claim to be a sovereign state.

In 2011, following a referendum, half of Sudan became a real, independent state, with UN membership and all. However, they are not doing any better than before they broke off from Sudan.

On 27 October 2017, following a referendum, the Government of Catalonia (until then an autonomous province of Spain on the border of France) unilaterally declared independence, and really pissed off the Spanish parliament. It's basically a left wing Brexit that has been brewing for 600 years.

In 1970 a smart Aussie farmer pissed off at the government for enacting wheat production quotas seceded from the Commonwealth of Australia, starting the Principality of Hutt River . On 2 December 1977 the Principality declared war on Australia, notifying authorities of the cessation of hostilities several days later, and wrote to the Governor-General and asserted that "Sovereignty is automatic to a country undefeated in a state of war...and if the state of war is not recognized by the other party, once the notice is given then these conventions apply to their relations." Despite solid legal grounding, friction with the Australian government continues to this day.