Apparently many people have found this room by accident.
The twins found it when they were looking for a place to hide from Filch; Dumbledore found it when he needed to go to the bathroom; hundreds of students found it when they were trying to hide something; Voldemort found it when he needed to hide a horcrux.
Books say that you open it by walking by it 3 times, but there's no way so many people would do so accidentally.
How does one find it in the first place, without being told about it?
The way to get in is precisely as you described.
If you think it's unlikely, think it through. Someone walks by once initially trying to find something in one direction. The second occurs when they can't find it and try another part of the castle. Third is when they're doubling back and trying just one more time where they already were. Poof, the castle helps out.
It's designed as a reward for the persistent, and a helper for the desperate. The castle sees plenty of both.
In the story, Dobby specifies that Harry has to walk by the room three times to get the Room of Requirement to answer him. But this is when Harry is doing it deliberately. The students that found out about the room were in great need, and the room (called the Room of Requirement) answered. Harry's need was not a life-and-death or a safe-and-punishment, but rather a search-and-search-again need.
Below are a few scenarios, from the book.
Dumbledore has an unusually full bladder and walks by the Room of Requirement. The Room of Requirement senses that he really needs to go the bathroom and appears.
Dumbledore did not walk back and forth three times asking for a room of chamber pots (although is sounds like something Dumbledore would do -).
Harry needs to find a room for DA. He walks to the Room of Requirement. The Room of Requirement senses that he does not have a great enough need and that he will walk back and forth three times. Therefore, the room waits for him to do the walking and asking.
Harry needs to hide his potions book. He runs to the Room of Requirement with great need. The room senses his need but knows that he will do the walking and asking because Harry thinks that walking (or running, in this case) is the only way to open the Room of Requirement.
