Much of the difficulty associated with the removal of wisdom teeth has to do with their positioning in the jaw (see types of impactions page). In general, the further through the gums a wisdom tooth has erupted the less involved both the extraction and the subsequent healing process will be. Don't necessarily expect the worst. Some wisdom teeth will be no more difficult for your dentist to extract than any other tooth. As part of your pre-extraction examination your dentist should be able to give you an idea of what to expect, both during the extraction procedure and subsequently during healing.
If there has been an active infection associated with a wisdom tooth (such as pericoronitis) a dentist will usually delay the timing of the extraction. In these instances your dentist will usually prescribe a course of antibiotics for you to take, typically for 7 days or so. The antibiotics will diminish the amount of infection which is present at the time of the extraction, thus allowing both the extraction process and your subsequent healing go more smoothly.
If a dentist can clearly ascertain that there are good reasons to remove a wisdom tooth, then it is usually best to go ahead and have it removed as soon as is reasonably possible. While there are no hard and fast rules regarding a specific age by which a person's wisdom teeth should be extracted, as a rule of thumb, the younger in age a person is when they have their wisdom teeth extracted the fewer the number of complications they experience.
If wisdom teeth can be removed in a person's later teens or early twenties there is a greater chance that the roots of the teeth will not yet be fully formed and the bone surrounding the teeth will be less dense. Both of these factors will make the extraction go easier. (Possibly the best time to have wisdom teeth extracted is when their roots are about one third to two thirds formed.)
Also, it seems that as we age we are simply less resilient. The healing process is usually more of an ordeal for "older" people than "younger" persons. Studies have shown that complications related to the extraction of wisdom teeth increase significantly as patients passes into their mid to late 20's.