Wall Running is a technique Sonic characters use to get to places they can't reach otherwise. They must be at full speed to do it though, and usually can't hold it for long.
Sonic's first real-world use of the move was in Sonic Adventure's Speed Highway, where he ran down a building, but since then has used it numerous times in the same manner, even repeating the same stunt for Sonic Adventure 2 in City Escape.
From Sonic Unleashed onward, he can control this technique and use it to run on waterfalls, along caverns and up skyscrapers. The Sonic Boost helps him stay at top speed to keep running on the wall, and even allows him to change direction.