Although there are various designs of watchmakers' lathe, some dating back to the late 1700s and including specialised models - for example "fiddle" lathes,  "steel turns", Jacot, Swiss, Swiss Universal (also called the English Mandrel) Bottum and Dracip - more modern examples can generally be divided into two types: the lighter "Geneva" and  heavier "WW". The "Geneva"  can be recognised by a round bed, with a flat machined along the back for its full length and nearly always supported on a single foot. These lathes, invented in 1859 by Charles S. Moseley in the U.S.A., generally take a 6mm or 8mm collet and were designed only for lighter, very high-precision work. The "WW" (Webster-Whitcombe), is the more popular and versatile machine and also of American origin, from around 1889. The centre height of the WW was usually 50 mm, though very occasionally 65, 70 mm and other figures are encountered. The bed was of heavy construction, formed with a 37 mm-wide flat on the top and a 60-degree bevel along each edge, and carried a headstock spindle to accept 8, 10mm or 12mm collets. Larger than the WW type are what might be called "toolmakers' or "bench precision" lathes: these vary in size from the Schaublin 65 and 70 (the latter being the most popular and frequently-encountered machine in the professional watchmaker's workshop) to larger examples such as the Schaublin 102 and models by makers such as Boley, Lorch, Leinen, Stark, American Watch Tool Company, B.C. Ames, Wade, Pratt & Whitney, Rivett, Cataract, Hardinge, Elgin, Hjorth, Potter, Remington, Sloan & Chace and others. Whilst useful machines in a precision workshop these are outside the scope of this article.
There were dozens of brands of watchmakers' lathes and a lot of "badge engineering" went on. This was compounded by accessories being interchangeable between makes so it is entirely possible that a lathe has been "made up" from others. However, it's very unlikely that the bed, headstock and tailstock will be from different manufacturers; if they are, be wary.
You can see other examples of watch and instrument makers' lathes and their accessories here:
http://www.lathes.co.uk/pultra
http://www.lathes.co.uk/boley/page3.html
http://www.lathes.co.uk/boley/page4.html
http://www.lathes.co.uk/boley/page5.html
http://www.lathes.co.uk/boley/page6.html
http://www.lathes.co.uk/boley/page7.html
http://www.lathes.co.uk/moseley
http://www.lathes.co.uk/bergeon
http://www.lathes.co.uk/btm
http://www.lathes.co.uk/levin (USA)
http://www.lathes.co.uk/derbyshire (USA)
http://www.lathes.co.uk/favorite
http://www.lathes.co.uk/ime
http://www.lathes.co.uk/lorchschmidt
http://www.lathes.co.uk/lorch
http://www.lathes.co.uk/derbyshire
http://www.lathes.co.uk/btm
http://www.lathes.co.uk/ime
http://www.lathes.co.uk/leinen
http://www.lathes.co.uk/rolls-royce

Availability
Watchmakers" or Instrument-makers' lathes can be very valuable, especially if they are in fine, original condition and complete with lots of accessories. Buying just a basic lathe with bed, headstock tailstock and T-type tool rest can be false economy - there are lots of these about, at attractively low prices, but the real value is in the extras that allow the lathe to be used as a miniature "machining centre" - as originally intended - to cut, for example, wheels (gears), mill small parts and hold tiny, awkwardly shaped mechanisms for repair and restoration. Because there is considerable competition for accessories, if your basic lathe has to be equipped one part at a time much time, effort and money will be expended - hence, if you can, find a fully-equipped lathe; this will be a much better investment and a lot easier for you, or your heirs, to sell.
If you are looking for one of these machine I would strong recommend advertising for one. There are thousands sitting unused whose owners will never get round to advertising them - a "wanted" advertisement might just encourage them to get in touch:
Accessories:
Typically, the most valuable watchmakers' or instrument-makers' lathe would still be in its original wooden box with a wide range of equipment including as many of the following as possible:
Compound slide rest - screw-feed or lever action
Collets - a set of around 20 "Wire" (often called "split chucks"),
Collets - "Wheel" type in a set of 5 or 6
Collets - "Ring Step" type in a set of 5 or 6
Box Chuck
Chuck conventional 3-jaw Self-centring  (sometimes called a "Universal Chuck") in ring-scroll (knurled ring round the outside) and key-operated models,
Chuck conventional 4-jaw Independent
Cutting tools - as large a collection as possible
The following "chucks" mounted on collets:
Chucks - balance
Chucks - box type with screws through the body to hold jobs
Chucks - brass split type (sometimes called jewel type) to fit inside larger steel collets
Chucks - button or crown usually in sets of 10
Chucks - carrier for driving work between centres
Chucks - circular-saw type
Chucks - emery wheel
Chucks - lantern in bronze or steel,
Chucks - wax
Chucks - wood screw
Chucks - wood turning
Compound Slide Rest
Drill chuck for headstock or tailstock use
Drilling plates - self-centring
Drive Plate
Eye glass on adjustable holder
Fixed steady
Jacot Drum
Lapping attachment
Pivoting attachment
Saw table
Sinking tools
"Mandrel" - this has the appearance of a spare headstock with a "faceplate" attached and is used for super-precision work
Micrometer-adjustable boring head
Milling and Grinding Spindle,
Pivot polisher
Pivoting attachment
Roller rest in single or double-wheel types
Rose cutters
Screwcutting Attachment with a set of Changewheels
Sinking tools
T-rest - the basic device to rest a tool against. Available in standard and tip-over types
Tailstock chucks - also known as "drill stocks" and available with flat heads, V heads and chuck type
Turning arbors
Topping or "rounding up" tool
Two types of Tailstock (sliding spindle and a lever-feed spindle),
Tip-over or simple sliding T-shaped Hand-rest,
Universal Faceplate and Pump Centre,
Vertical milling Slide,
Wheel-cutting attachment with division plate (to cut what the laymen would call gears but which are known to the watchmaker as "wheels").
Drive systems
Even when fully equipped it is not unusual to find that a watchmaker's lathe has no drive system or even motor. However, this is rarely a problem for the easiest and cheapest solution is to use either the motor from a sewing machine or, preferably, a proper "Parvalux" unit - the latter available in 1-phase, 3-phase and DC types with speed ranges spanning 0.2 to 10,000 r.p.m. The motor can be bolted in place behind the headstock and driven by a special Swiss-made round plastic belt that can be flipped easily from pulley groove to pulley grove, there being no need to make up the type of hinged countershaft that a larger lathe would need. The writer can supply Parvalux motors their controller and the special belting
Handbooks
Unfortunately no maker of a watch lathes has ever offered a proper handbook for their products but, happily, there is an excellent hard-back book available that does the same job: "The Watchmakers' Lathe".  This is a long-established publication and, because most of these lathes were built along the same lines, and use almost identical accessories, the book is able to give precise instructions that apply to all types.
UK post-paid delivery: £18.75 EU post-paid delivery: £19.75 World-wide air-mail delivery: £26 (about US$67) email to order

Manufacturers and Brands
Genuinely high-quality Watchmakers' lathes were manufactured and branded by, amongst others:
Accro
Adams George
American Watch Company (C. S. Moseley-designed lathe circa 1859)
American Watch Company (A. Webster-designed lathe circa 1859/60)
American Watch Tool Company (Webster-Whiitcomb improved-design lathe of 1889 - the WW model)
Ames
ARS
Bergeon
Boley
Boley-Leinen
Boston Watch Company (C. S. Moseley-designed lathe circa 1858)
Bottum
Boydon
B.T.M.
Cataract (Hardinge)
C.L.H.
Coronet
Derbyshire
Dracup
E.H.J. (E. H. Jones machinery dealers and commissioners)
E.M.E.
Favorite
Gamma
Gem (Gem Glorious)
Gentil (Star Lathes, Switzerland)
George Adams (re-branded Boley and Lorch, etc. and cheaper imitations under his own label)
Hardinge (Cataract)
Hammel, Riglander & Co.
Hopkins
IME
Jones (J & T Jones UK)
Lampert (U.S.A.)
Lanco (Lane Cove)
Leinen
Levin
Lorch (Lorch Schmidt)
Manhora
Mansfield
Marshall
Moseley
Nordan
Ohio
Paulson
Peerless
Perton
Precista
Pultra
Reliance
Rivett
Schaublin
Schmidt
Scomea (Société Commerciale d'Outillage et de Mécanique d'Aviation)
Simplex
Sloan & Chace
Star (R. Gentil & Co. Company of La Brevine in Switzerland)
Stark
Steiner
Swan
Taylor
T.C.M.
Waltham
Webster
Webster-Whitcombe (WW)
Whitcombe
Wiskum
Wolf, Jahn
Some of these are featured in the Machine Tool Archive