An adult human typically has 32 teeth. All but 4 of those teeth typically arrive during childhood, before the age of 10. The remaining 4 teeth are the mandibular third molars, more commonly known in English as "Wisdom Teeth". Wisdom teeth typically erupt from the gumline approximately between 18-20 years of age. The etymology of the name revolves around the idea that people get their wisdom teeth after they have gained some wisdom.
Where I grew up, and across much of the 'westernized' world, Wisdom teeth are removed during early adolescence or early adulthood as a purely preventative measure. Wisdom teeth that come in wrong in some way can lead to the crowding of other teeth, infection, impaction, and other problems. However, more recently, several studies have been attempting to determine whether preventative removal of wisdom teeth is appropriate. This summary in the Cochrane Library suggests that there is no reason to remove wisdom teeth until they are causing problems, although the data is apparently very limited.
In my case, the early prognosis from my dentists when I was in high school and college was that my wisdom teeth would come in with no problems. Considering both my parents had wisdom teeth problems, my sister did, and all my relatives on my mom's side did, I should have expected that these teeth would need to be removed eventually. Six years ago I had a wisdom tooth come in Mesioangular impacted, which means it came in facing the front of my mouth (see images on the Wikipedia article for reference). This is apparently the most common orientation of impacted wisdom teeth, and has the potential to crowd or damage the other molars. In my case, since I basically did nothing for 6 years, so I probably have some damage on my 2nd molar. Here's to hoping that's minimal.
I've been unable to find good data on what proportion of individuals have wisdom teeth that are impacted or the proportion that just have them removed (impacted or not). Some recent studies have suggested that even if they aren't causing obvious problems, they may be detrimental. WebMD suggests not removing them at all if you are over 30 and haven't had any problems. Partly this is because not all wisdom teeth pose problems, and partly it is because the older you are, the more the bones around your wisdom teeth have hardened and the longer and more painful the recovery is. Past a certain age, I imagine wisdom teeth are simply not removed.
A huge amount of variation exists among different human populations in the occurance of wisdom teeth (and in the number and arrangement of teeth in general). Citations in this PNAS study (which is really talking about the genetic controls over tooth formation) indicate a range from 0.2 % occurrence for Bantu speakers of Angola to virtually 100% in Mexican Indians.
The whole idea of wisdom teeth is a strong bit of evidence for the continued adaptation of humans to their environment. The exact mechanism for the changes in human jawbones is not clear, but it definitely seems to be related to diet (short discussions here and here). As humans began eating less coarse foods, the jaws began getting smaller, and the teeth (controlled by a different gene) did not have enough room to all fit in the jaw without problems.
I've actually known a number of people who've had their wisdom teeth function perfectly normally. When I was getting a blood test last week in preparation for my wisdom teeth removal, the lady who was taking my blood said that she lost her 2nd molar, and the 3rd molar (wisdom tooth) filled the opening this created and she got good use out of it for 20 years (eventually she had to have it removed...maybe she doesn't brush?). I've heard a few people whose wisdom teeth came in just fine, no problems at all. I'm not really sure how frequently any of these things happen, and I don't have access to very good medical journals.
I was fairly terrified about the prospect of getting my wisdom teeth removed. I've never been under general anesthetic before, and both my sister and dad have had some problems coming out of general anesthetic in surgeries they've had. Plus, there are a number of painful and annoying impacts of the surgery: Swelling, bleeding, and possible nerve or sinus damage. Problems which are more likely the older you are, and I've been feeling very old lately (I just turned 30).
I'm writing this on Tuesday, and I had the surgery on Monday, and I can tell you that my fears were vastly overblown. The surgery itself was brief, painless, and even though I was partially aware during the procedure (turns out it is not a true general anesthetic), I felt no pain or nervousness once sedated. Yesterday I felt great when I got home, and have have very little lingering pain. Today, especially this afternoon and evening, have been a lot more painful, but I think part of that has had to do with me wanting to avoid the pain meds as much as possible. I've also not eaten much, simply because I'm already sick of ice cream, yogurt, smoothies, etc.
Overall, if you're considering this surgery at the advice of a dentist or doctor, I recommend you do it immediately. I've had several painful experiences in my life (ulcer, concussion, foot surgery) and this is no-where near that level of pain and discomfort. Its more like 'persistent headache' than 'injured'. I think that if you need it done, its probably better to get it over with as soon as practical instead of waiting (yes, I'm talking to you!).
Some other references and guides to the whole wisdom tooth removal process: