Text quoted from The New Discworld Companion.

Igor. Everyone who is (or was) anyone in Uberwald has an Igor as a servant. Uberwald's servant class is heavily populated with extremely similar-looking assistants, all of whom are called Igor, to save confusion. At least, to save confusion amongst Igors.
     They are in fact a clan which, instead of myths and legends, passes on the secrets of incredibly skilled surgery (except in the area of cosmetics), plus various associated hints and tips, often to do with weird chemistry and lightning rods. he Igors effectively treat their own bodies as the common property of all Igors and they would hope that any useful bits they have will be passed on to their relatives; Igors do not so much die as get broken down for spares.
     For reasons that have never satisfactorily been explained, Igrs seem very popular with the ladies and, bizarrely perhaps, their daughters (Igorinas) tend to be very pretty. Igorinas sometimes learn the skills, although they refrain from the lisping and the very visible stitching; those are not necessary in any case, but are the Igor equivalent of tribal markings.
     Although classically Igors are to be found working for insane geniuses living in draughty castles, they give freely of their time and talent to anyone in need. Many a life or livelihood has been saved by a carefully grafted-on foot, arm or head. However, the Igors are firm believers in the principle of 'what goes aruond, comes around' and, whenever possible, they assume and expect that anyone helped by them will, when the time finally comes, see their way clear to letting any local Igor have a quick rummage for any organs worth recovering. Thus, Igors are very respected in Uberwald; they may look like a road accident, but a good Igor could probably get an uncooked sausage to grunt and hunt truffles.
     The Igors have now formed an agency, We R Igors ('A Spare Hand When Needed'), based at the Old Rathaus, Bad Shüschein (c-mail: Yethmarthter Uberwald). The code of the Igors is very strict - Never Contradict. Never Complain. Never Make Personal Remarks. Never, Ever Ask Questions. Never Oil Doors.
     Igors are loyal, but they are not stupid. A job is a job. When an employer has no further use for your services, for example because he's just been staked through the heart by a crowd of angry villagers, it's time to move on before they decide that you ought to be on the next stake. An Igor soon learnd a secret way out of any castle and where to stash an overnight bag. In the words of one of the founding Igors: 'We belong dead? Ecthcuthe me? Where doth it thay "we"?
     In the course of the books, we have met a variety of Igors, including:
     The de Magpyr Igor. Like most Igors, he has a lisp and walks with a limp. His hand is a mass of scars and stiches and he has a geometrically interesting smile because of the row of stitches right across his face. He has two thumbs on his right hand and two hearts (one, it is thought, a bequest from a Mr Swines; installing his own second heart is something an Igor does early in his career). His feet were a bequest from a Mikhail Zwenitz. He has installed a metal plate in his head, wired down to his boots in case of lightning strikes. (Carpe Jugulum)
     The Embassy Igor. His eyes are different colours, unlike those of his cousin at Lady Margolotta's. (The Fifth Elephant)
     Jeremy Clockson's Igor. He has the traditional blackened fingernails and was sent to work for Jeremy by Lady Lejean. His gransfather, with a Demented Doctor Wingle, built the first Glass Clock of Bad Schüschein. Before working for Jeremy, he had worked for Mad Doctor Scoop, Crazed Baron Haha, Screaming Doctor Berserk, Nipsie the Impaler, Dribbling Doctor Vibes and Baron Finkelstein. This is a fairly normal résumé for an Igor, and rather than indicating a footloose nature it merely recognises that, quite often, the mob wins. (Thief of Time)
     Lady Margolotta's Igor. As he says himself, he is Igor, son of Igor, nephew of several Igors, brother of Igors and cousin of more Igors. Although he wears the traditional shabby black tailcoat, he has both eyes the same colour, which suggest a young Igor just starting out.
     The von Uberwald Igor. (The Fifth Elephant)
     The Watch Igor. Nephew of the Embassy Igor and constable in the City Watch, although strictly speaking he is a forensic specialist and Watch medic. He's quite young-looking. Like many Igors, he has his eyes on different levels. One ear is larger than the other and his face is a network of scars. He has a deformed hairstyle - greasy black hair brushed forward into an overhanging quiff of excessive length and with a 'DA' at the back. He enhances his Igor clothing with a pair of crepe-soled shoes. He has two thumbs on his right hand and two hearts. He thinks of himself as quite modern and every so often forgets to lisp. Being at the forefront of Igoring, he is a keen genetic experimenter and his gloomy cellar generally has an angry tomato or enraged experimental leek in it somewhere.

Hyel's addendum

The Monstrous Regiment Igorina. See Igorina.
     Reacher Gilt's Igor. (Going Postal)