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I am interested in macro-photography. I see there are macro telephoto (zoom?) lenses (e.g. 200mm), or smaller macro lenses (e.g. 40mm) ...
What are the different types of macro lenses and their advantages? Which one is recommended for the best rendition?
"What are the different types of macro lenses"?
There are "Macro" lenses and there are Macro lenses. As others have mentioned, a true Macro lens will magnify the subject to a 1:1 ratio which is generally a desirable feature. Many lenses will be marketed as 'Macro' lenses even though they don't magnify down to 1:1 so be careful to check the actual magnification factor of the lens you're interested in purchasing.
"What are the different advantages?"
Two important factors when considering a macro lens are the magnification factor and the aperture range. Lenses with a higher magnification ratio, 1:1 or even 5:1 are useful for small or detailed subjects and lenses that have apertures down to f45 or f64 can create a larger depth of field. As a side note, the ability to magnify down to 1:1 isn't necessarily critical for all macro work and if you're open to slightly lower magnification, 1:2 say, you can use Tilt-Shift lenses or Zeiss optics that open up to f2.0. Or, since 1:1 macro lenses tend to be primes, you can use one of many zoom 'Macro' lenses that have lower magnification.
"What is recommended for the best rendition?"
Well thats a tough question that depends on what kind of work you plan on doing. If you plan on photographing insects or anything that might fly off or bite you, you'll want a larger working distance from the subject so you'll want to look at the 150-180mm range of macro lenses, or even using a 300mm lens. The downside to a longer focal length is camera shake and vibration will be more of a problem which can drive you towards the 50-65mm range of lenses. Of course the problem there is not only are you so close to your subject you could scare it, but you can block the light with your camera. I personally feel that the 90-105mm area is the best compromise of working distance and vibration/camera shake, plus in that area there are several lenses that offer image stabilization for shooting hand-held.
The accepted definition of a macro lens is a lens that can focus close enough in order to achieve a 1:1 reproduction ratio, that is project an image on the film plane or sensor that is the same size as the object.
This means with a standard APS-C DSLR you can fill the frame with an object only 22mm across. This applies to macro lenses of any focal length, however the longer the focal length the further you can be from the subject whilst still filling the frame.
This is known as the working distance. Having a large working distance conveys many advantages, not disturbing wildlife, and not blocking the light to your subject are amongst them. You also receive the advantages of a longer focal length, namely prespective compression (known as foreshortening), and sharpness corner to corner.
Wider focal length macros may have larger apertures, and offer deeper depth of field which can be advantageous. You also get the opposite effect to foreshortening, which can be an interesting effect.
If you also plan to use your macro lens at non-macro distances then you may also want to consider what focal lengths are missing from your setup.
There is no possible answer to which is best because all macro lenses are not the same. Most macro lenses are very good, sharp and low distortion. Some may be even better.
For the focal-length, the difference is distance. With 40mm macro you have to be very close. Some subjects fly away! With 100mm not so close and 200mm more space but faster shutter-speed or stabilization needed.
Important to look for magnification. If it says 1:1 it is real macro. Sometimes it says 1:2 so it cannot capture as small subject. One one Canon does better with 5:1, see blog here. Very nice looking but difficult and must be very close to subject and only focus is manual.
EDIT:
Real macro lens are mostly prime, zooms rarely have good magnification. Cannot find 1:1 magnification zoom, only 1:2, so zooms do not show the subject so close. Aperture is better on prime, F/2.8 is usual for macro. Can give more shallow depth of field compared to macro zooms.
As others have said, the main practical difference between true (1:1 or greater magnification) macro lenses is the distance to the subject required to achieve the desired magnification. In general, long macro lenses do not directly affect depth of field or most other parameters of the image.
The main advantage of the longer focal lengths therefore, is that the greater "working" distance allows you to capture images of shy, skittish or dangerous subjects, such as insects or scorpions. It also allows you to use the on-camera flash without the lens barrel shadowing your subject.
However, longer focal length also means more shake. Since your typical macro shot will be taken at a very narrow aperture (f/11-f/16 is common on full-frame/APS-C, f/22-f/32 are not unheard of), your shutter speed will of necessity be slow. Nikon and Canon have attempted to combat this with their ~100mm macros (Nikkor 105mm f/2.8G ED IF AF-S VR and the Canon EF 100mm f/2.8 L IS USM Macro), while other manufacturers have in-body image stabilization to mitigate this problem.
However, the focal length of a macro lens does affect the final image in a rather subtle way.
Due to perspective compression artifacts caused by the distance from the subject, images shot with longer macro lenses tend to have a more blurred background. See the below example from http://the-digital-picture.com for an illustration of this effect.
The other answers are spot on (so read them first). However, they're missing one other important element which is subject isolation. Some feel that this is less important in macro photography, so they don't mind a 50-60mm macro lens as sometimes want a wide background to show the environment of the subject. However, other times the background is highly distracting and the less you can get behind it the better. Blurring the subject is only one way to do this and doesn't always work when the distance to the background is not high in the first place. So the other option is to reduce the angle of view, which obviously means increasing the length of the lens.
(Personally, I use a 100mm macro lens as a good compromise. Sometimes I wish I had something longer, but rarely do I want something shorter).
