The are two optional characters that you can obtain during your playthrough of Final Fantasy VII named Yuffie and Vincent. Information for obtaining each is included below.
The first optional secret character that you can obtain. She is randomly encountered in the forested areas of the game starting with the one outside the Junon Area.
Vincent can be found slumbering in the basement of the Shinra Mansion in Nibelheim. Obtaining him involves opening a safe, battling a monster and using the key in the safe to unlock Vincent’s chambers.