Limbs were important appendages of organic bodies and many types of mechanical chassis. They were typically designed for motion and/or manipulation, and were found on most sentient and non-sentient species throughout the galaxy, and many droids and other artificial constructs.
Humans and many other important sentient species were bipedal, with two legs and two arms, and this form was imitated by many droids; but there were many variations. Sometimes these were relatively subtle, especially in the construction of hands, feet and their digits.
Other species and designs, however, had limbs of more radically different designs, like the dianoga with its tentacles and prehensile eyestalk, or the R-series astromech, which could travel in a bipedal or tripodal configuration, and had a wide variety of manipulator arms that could be extended from their torso and head.
Every Star Wars movie but The Phantom Menace features dismemberment, of either organic or artificial limbs. Rob Coleman discusses this in the Attack of the Clones commentary track ("Yet another in the series of Star Wars severed limbs. I've actually tried to talk to George about the whole reason for the severed limbs in these movies and he always just sort of smiles and chuckles and never gives me the real answer.") and when asked by Vanity Fair about the dismemberments, George Lucas answered: "That's what happens when you play with swords."