By itself, nicotine is generally considered to be relatively safe for adults, although it can cause various side effects, such as headaches or increased heart rate. However, nicotine can interfere with the development of an unborn baby, which is why pregnant women should never use any product that contains it.
Most doctors believe that the effects of nicotine are most similar to the effects of caffeine, in that they lead to a quick burst of energy and temporarily raise the heart rate. Studies have yet to show any direct link between nicotine and increased risk of cancer, while nicotine use only leads to a minimal risk of cardiovascular problems as well.
The real problem is that most people use nicotine through smoking tobacco, but it is actually the smoke, not the nicotine that leads to health problems. This makes studying the effects of nicotine slightly more difficult, as the majority of nicotine users are smokers. Still, if nicotine were terribly harmful, then using smokeless tobacco would also be terribly harmful, but this doesn't seem to be the case. This isn't to say that smokeless tobacco doesn't sometimes lead to cancer, but it is generally thought that the nicotine doesn't play a major role in cancer development.