Well, there is Bir Tawil, a bit of land between Egypt and Sudan. Neither county claims it, and no one lives there.
From Wikipedia:
The declaration of independence was made by Jeremiah Heaton, a former Democratic Party Congressional from Abingdon, Virginia, who made a 14-hour overland trek via desert caravan to a remote, disputed shard of territory between Sudan and Egypt, planted a flag, and declared it, provisionally, “The Heaton” and later, officially, on a suggestion from his children, the Kingdom of North Sudan. The piece of land in question is Bir Tawil, an 800-square-mile lozenge of desert. The reason Heaton has made himself king of North Sudan is to fulfill a promise to his seven-year-old daughter, Emily Heaton. As the self-styled monarch told the press, “Over the winter, Emily and I were playing, and she has a fixation on princesses. She asked me, in all seriousness, if she’d be a real princess someday. And I said she would.”
Now that's an indulgent father!