I have never built a robot that can drive through a maze and solve it, but I know that there are some algorithms to do so. Over at the blog PATRICK MCCABE MAKES, Patrick shows a great, relatively simple algorithm to solve the maze using a technique he calls "left hand on the wall."
The robot travels through the maze once and maps a fairly good portion of it until it gets to the finish. And then using a system to process the map, he is able to have his robot find a shorter way through the maze. Then using that information, the robot easily navigates the maze in quick fashion. It's an easy to read tutorial. I like it a lot. I don't think it is the most efficient way to solve a maze, and I think that using this method might not always take the very best route, but it will certainly get to the finish.
Click here to zoom over to his site.