Count or countess was a title given to members of some royal families, such as those of Old Britain.
In 2266, Harry Mudd promised Magda Kovacs that upon wedding a lithium miner she'd be (as rich as) a countess. (TOS: "Mudd's Women")
Will Riker told a joke about a count who was about to be executed by a headsman. (TNG: "Data's Day")
Regina Barthalomew, a holographic character who was part of Sherlock Holmes Program 3A, was a countess. (TNG: "Ship In A Bottle")