There's many of these so called illegitimate countries around the world. I've been reading of many in a recent book I picked up.
The most famous I'd imagine would be the Principality Of Sealand, a WW2 Naval sea fort which was commandeered by British Army General Paddy Roy Bates in 1967. The fort at the time was situated outside of British Territorial waters and they claim that they've been recognised de facto by the UK. In 1987 the UK extended their territorial waters but didn't interfere with Sealand. They have their own Constitution, Flag and anthem and they follow the British Common Law system. Also a currency the Sealandic Dollar.
They sell coins, postage stamps, Passports, Lordships and Ladyships and other titles of Nobility to raise funds, they also have hosted pirate radio stations in the past. Tourist bookings are also taken and they're plans for a Casino to open on the platform
Sports wise they field a football team, an associate member of NFB, the sanctioning body of FIFA for non recognised States.
Some of these so called Nations seem like the dreams of a madman, others's you'd kinda of half admire. It's an interesting topic.