This article is from the of the muppets FAQ, by Craig Silverstein with numerous contributions by others.
You may have noticed that Muppets, particularly Muppet musicians, tend to do everything with their left arms. This is because most Muppet performers are right handed and use their primary hand to control the head and face of the Muppet. (Louise Gold is one of the few left-handed performer, and her Muppets are right handed.) This leaves them their left hand to control the Muppet's arms. Muppets like the Swedish Chef, which are controlled by two performers, are of course an exception.