Several characters in the Ranma manga are Dojo Yaburi - Dojo Challengers. The most remembered one is the one with his own story arc but there were others Ryoga did so when he had the mark of the gods, Ryu Kumon was one, Ranma may have been one prior to coming to the Tendo's, and the Tendo's openly display a sign inviting anyone to challenge their dojo.
While not all that uncommon in fighting manga/anime and martial arts movies (there even is a movie with Dojo Yaburi as it's title - I haven't seen it) in real life it is an outdated practice. It was at one time pretty common. An example of a real person who was a dojo destroyer is Souke Teruo Hayashi the founder of Hayashi-Ha Shito-Ryu was one prior to starting his martial arts school.
A Dojo Yaburi is a person who challenges the sensei, and typically any students present, to kumite (sparing). There are many reasons for such a challenge, but typically they range from attempting to humiliate the sensei and steal students to ascertaining if the school has anything to teach the challenger. The reason for the Dojo Destroyer to do so in the Ranma manga was never given, he appeared to just like destroying dojos. Ryoga and Ranma seemed to do so to learn their styles (Ranma, for example, has demonstrated that he can learn a style by having the opponent fight him).
The common means of going about this is to enter a dojo and request to fight the head instructor. Some dojo's would not accept challenges, others would. Most commonly the ones that do accept would first require the challenger to fight the two highest ranked students. If the challenger was successful in this endeavor the headmaster would then fight the challenger. In martial arts entertainment it is common for the challenger to then take the dojo's sign publicly humiliating the dojo.
Karateka that issue a dojo challenge are commonly considered to be hoodlums of one sort or another and it was common to bar such individuals from entering a dojo. This is rarely done anymore, though they still do exist in some forms. Like asking for an exhibition match between head instructors from competing schools.
There is also another type of dojo challenge in which a martial arts dojo master would test perspective students, to weed out unwanted students. Though this is even less common (not the testing of students, turning students away since most places will take pretty much anyone).