Many health benefits have been claimed for ginseng, but, as with many other traditional remedies, little has been proven. As ginseng is a plant that is freely able to grow by anyone, there is little incentive for drug companies to invest in large-scale trials, which means that most of the studies we have are the efforts of enthusiastic amateurs and perhaps-biased Chinese researchers.
The primary health benefit claimed for ginseng is that it reduces stress without otherwise harming the body something like alcohol, only without the side effects. The few studies that have been done have shown a few other benefits: it was proven to slightly reduce the risk of flu in old people, for example. The most controversial claim (again, one that is made for many traditional medicines) is that ginseng helps to fight cancer but while this has been shown to be true in animals, it does not seem to have any effect in humans.
Red ginseng has a few extra health benefits: it even further reduces the risk of cancer in some animals, and has also been proven to be an effective treatment for impotence, although nowhere near as effective as real impotence medicines such as Viagra. Similarly, wild ginseng has the same effects as normal, domestic ginseng, but is a lot more powerful. Many of the problems with studying ginseng come from the sheer number of different types on the market and different places they are grown, as every variety seems to produce slightly different effects.
Studies from China make somewhat vaguer claims for ginseng, including one government-funded study that concluded that ginseng increases quality of life. It seems likely that this is more of an attempt to promote Chinese agriculture than anything, however.
In the end, the only real proven benefit for ginseng is that it reduces stress, and, indeed, this is the reason most people take it. As a stress treatment, ginseng can be very good, but dont expect the world from it.