Yamashita,
Your question is a bit complex and isn't as straightforward as better or worse. I'll deal with that after dealing with a few of the things that have already been mentioned in reply.
Sulhan,
The size of the lens has no real direct relation to the number of elements and groups. Instead, it is really the optical complexity of the lens. Telephoto prime lenses which are relatively simple to correct optically require few elements and groups, despite their vast physical size. A small superwide angle lens can require two to three times the number of elements and groups as a telephoto with the same aperture 60 times its weight because of the difficulty in correcting wide angle lenses.
Zoom lenses, by nature of their complex optical formula in needing to correct aberrations across a range of focal lengths, mean that they all tend to have a relatively large amount of elements and groups. It follows that the larger the zoom range, the higher the number of elements and groups as a general rule. Zooms that cross different focal length groupings (wide to normal to tele) also have an abnormally high number of groups and elements because optically, a wide angle lens is very different from a telephoto lens.
Sulhan is right in that a lens with more elements and groups can be a slower lens. An aperture is a physical measurement of the lens iris that is (or should be) accurate from lens to lens. However, the amount of glass surfaces present in the lens will limit the amount of light transmitted to the film plane, and also reduce contrast of the resulting image. As with filters, each element will entail light passing from air to glass back to air again, with light loss to minor transmission flaws, reflection, and refraction. Depending on how well an element is coated, the loss can range from a negligible amount, to about 3% of the light reaching the lens element.
Multiply that figure by 15 times in your average zoom lens, and you can see how a lot of light can be lost, compared with a lens that only has 6 elements.
Aspherical elements are not really needed to correct for distortions in long lenses, unlike what was suggested by Sulhan. They are more helpful in dealing with the distortion caused by wide angle lenses.
Apochromatic and Low Dispersion glass are actually the same thing. Tamron uses LD to designate their lenses with apochromatic glass in it.
More glass doesn't mean high cost, not in the sense that we are discussing here (elements and groups). Better glass, however, does mean drastically higher cost. While a bundle of small elements and groups (in your average 28-200mm superzoom costing $450 for example) can be relatively cheap, the same amount of elements and groups in a good quality wide angle prime lens, say in the 18-20mm area, can cost twice as much if not far more (the Nikon 18mm for example).
Internal Focus has nothing to do with creative mechanical movements. The issue is not in getting the mechanics to drive an internal part of a lens, that is straightforward. The big difference is designing an optical formula whereby the focusing group is inside the lens. This means a whole rework of a lens' optical formula, and is not as simple as simply taking the glass off the front or the back, putting it in the middle, and then finding some creative mechanical movement to be able to move that group of elements.
Be careful about what you read on the Net (including this post for instance), don't accept everything as gospel truth, and more importantly, when you read something, make sure you're understanding it properly and avoid the broken telephone syndrome, so you're not passing on spurious information.
Lens barrels are made from polycarbonate, yes. Lenses are still by and large made from glass, so I wouldn't worry too much about it. The main area where plastic is used is in the manufacture of hybrid ashperical lens elements. Molded and ground glass aspherical elements can be notoriously expensive to manufacture (and as already stated elsewhere is at least one reason explaining the relative expense of the Nikkor 20-35mm f2.8 compared to the AF-S 17-35mm; in fact the aforementioned Nikkor 18mm also uses either a ground or molded aspherical element, exactly which eludes me at the moment but a quick look at a Nikon source will reveal).
Of course, it helps if you understand what an aspherical lens is to start with, which will allow you to understand why they are so costly to mold or grind.
As a result, cheaper lenses like the 28-200 utilise hybrid (not hybris [sic]) aspherical elements (not lenses), which is basically a standard optically designed piece of glass, which is mated to plastic piece that produces the required aspherical geometry.
Denizenx,
I'm not altogether sure you're making sense, certainly I am struggling to understand you, but of course it could (honestly) just be me.
Now to answer the original question. More pieces of glass increases the chances of optical imperfections etc. It also reduces light transmission as mentioned. However with some lenses, you need to have many elements and groups to correct the lens optically, particularly with zoom lenses. So it really is a trade off.
Essentially, I wouldn't worry too much about the number of elements and groups in a lens, as the engineers would have made all the design decisions with lots of experience and backed up by computers with a large amount of information at their disposal. Chances are the elements and groups your lens has are the best solution for the given price and focal length.