Gibson USA used to have a section on their website called discontinued models. The new website is much more difficult to find information about specific models, and is geared more towards a marketing approach rather than a customer service approach. This makes it somewhat difficult to get the facts on some specific models both past and present. The website is more like the shopping trolley that won't go straight. You end up being taken in different directions and dazzled with products you don't need.
An alternative to the Gibson site is to do a general web search for the model in question. Often you will get lucky and get a discontinued item hit at one of the major online music retailers in the USA. They will have the model in question, some photos and the list of standard Gibson information. Of course the trick is finding just the right model. This is where the old Gibson site was a very good resource however, the problem still remains as to which specific model you have. It's not enough to say it's a Les Paul as there are many varieties within each of the specific catagories of Special, Studio, Classic, Standard, Custom, Supreme.
The Special will always have a flat topped mahogany body and two pickups. Other than that the specs vary in many ways such as neck binding or not, dot inlays or mini trapazoids, P90, P100 or 490R/498T Humbucker pickups, double cut or single cut bodies, faded finishes, gloss finishes or AA flame maple tops.
The Studio will always have a carved top and two pickups. The top may be mahogany on the faded models, but typically is maple on the gloss finishes. There are also various Smartwood series which had exotic sustainable forrestry timbres as a promotion for, well sustainable forrestry. The thing is all Gibson timber is from sustainable forrests but hey, don't let that get in the way of good marketing. The pickups may be P90's such as on the Gem series, or more usually the 490R/498T humbucker combination. They typically have fullsized trapazoidal inlays on the fretboard although I am sure I played one with dot markers in a store around 2000. Others had the mini trapazoids. Currently however (2001 ;) ->2010) they have large trapazoidal inlays. They have a 50's rounded neck profile without binding.
On the subject of neck profiles there are a number of different types. Typically you see two types in comon use. There is the 60's slim taper and the 50's rounded profile. There is also the 59 slim taper, and 59 rounded. The order of fatness is 59 slim, 60 slim, 50 round, 59 round. They also have the 60/30 on the ES339 which is slim tapered but a little thicker. The main differences between the 60's slim taper and the 50's rounded are the taper and the shape. They each start out at around the same thickness at the headstock end. As you move up the neck the 60's slim taper doesn't increase in thickness very much. The 50's rounded increases from around 20 up to around 24mm towards the body end of the neck (go look it up for exact specs) . The cross sectional shape of the 60's is a little like a D so it's got a flatter section in the middle of the neck. The 50's rounded is more like a C so it maintains it's curvature around the back of the neck. Each one has a 12" fretboard radius. The rarer 59 slim is like a 60's slim but thinner. The 59 round is like the 50 round but thicker. The original limited edition Les Paul Standard DC models which came in Tangerineburst/Gold and Lemonburst/Nickel finishes had the 59 slim taper. These two were in the same store as the Studio with dots. That's how I know about them as I looked them up on the Gibson site at the time. The later DC standards had the 60's slim taper.
The Standard is the model with a carved maple top and it may have a choice of either the 60's slim taper or the 50's rounded neck profiles. This appears on a sticker on the trussrod cover which makes identification easy at a glance. Anyone who knows Gibsons will tell by feel what the neck is so don't be worred if a second hand model has no sticker. If concerned greatly and the seller has no idea, get them to measure the thickness at the 12th fret. They are distinctly different for each. Personally I have found that the 50's rounded is very comfortable to play on and the rounded parts fits your hand nicely. It's a bit like how I don't like the Ibanez Wizard II necks which are completly flat in the middle. That's an extreme case of zero playing comfort. Anyway, if you are buying a Gibson it's all about the tone. It's the tone of Gibson guitars that sets them far appart from anything else ever made. Once you chase tone you will find yourself drawn to a Gibson every single time ;)
Some things to look out for. If the guitar has gold hardware with cream pickup rings then the screws on those pickup rings will be gold. If the guitar has gold hardware with black pickup rings then the screws on those pickup rings will be black. If you ever see gold (or silver) screws on a black pickup rings it's a fake. Look for knob and switch placement with attention to the alignment of the knobs. The Les Paul template has not changed so if the knobs don't look like they are in the just the right spots it's a fake. Les Paul Supreme models have no rear control access plate. Get a photo of the back of any supreme. If it's got a plate it's a fake. Custom models always have the metal tulip shaped tuners. If they are kidney shaped it's a fake. The year of manufacture of a Gibson is given in the serial number as the first and forth digits. For example 02371458 would be a 2001 model. Gibson cases were brown with a pink interior for many years from 1990 - 2005. Before that in the 80's they had these plastic molded handle type cases, and after the brown they now use a black one with a white interior. They are all TKL cases made in Canada. The case will have a TKL embossed tongue on the compartment lid. If it's a described as a Gibson Les Paul with one bad photo and the guys got no feedback ask for more pictures. Ask how long they owned it, where they got it, more pictures please. I've never seen anyone who I said that's a fake to say anything other than no it's not if they even reply at all. 99% of the time the seller knows it's a fake and the other 1% reply saying I don't know what you mean. If it's being shipped from China it's going to be a fake. Go to an authorised dealer to familiarise yourself with the feel and tone. When buying perhaps start off with a cheaper Gibson model like a Special to get an idea of the feel and sound yourself. Nobody seems to fake the Special models. The Studio is the best value model as you get a Les Paul sound and a hard case for less than a Standard. However if you want a standard don't settle for a studio as you will regret it for years. Better to wait it out with a Special that is cheaper to buy, easier to sell when the time comes, and sounds so damn good anyway that you may never sell it :)
Now if I could only work out how to add photos (it's not working) then I could put pictures of these models I've mentioned that I've owned or played first hand. As I said there are a lot of models even under the heading Les Paul subheading Special, Studio, Standard.
Customs are more straight forward. They are now made in the Custom Shop, for what reason I have no idea (marketing?). They feature an ebony fretboard with rectangular fretboard inlays. At one time they came in Black, White and later Red. I'm not into customs due to the price/sound ratio but again just do a general web search for the custom model. The headstock is also shaped differently as well as fully bound. The hardware is always gold, and the tuners as mentioned above are the metal tulip type ones. Incidently the White Studio models also have an ebony fretboard. This further pushes it up there for value/sound ratio if you want that sort of sound. Ebony is a bit brighter and has more attack than Rosewood which is a more rounded tone. Personally I love my White Studio.