They can be found in Ventureland, Lonesome Manor and Tomorrow City. The ones in Ventureland as mentioned above are mechanized pirates (they also reappear in the Train Tunnels). In Lonesome Manor, they are the Skeletons (who also appear in Epic Mickey) probably based off the short cartoon The Skeleton Dance. In Tomorrow City, the Bashers are dressed as Maximilian from The Black Hole.
To defeat a Basher, it is best to use Thinner to erase their armor. It will then spin to attack Mickey, exposing its weak point at the front, where it is vulnerable to a spin. Alternatively, it is possible to sneak up behind one and land a hit on its weak point before it can paint its armor in. Paint is mostly useless against Bashers, but it will slow them down.
In the second game, a new variety appears, based on Tik-Tok from Return to Oz and in the credits an unused chef Basher appears (most likely based on the one from the Autopia ride). The unused chef Basher also appears on a sign in Autotopia.