Nature and Wildlife photography has to be my favorite type of photography. It is a broad term which basically encompasses almost every type of outdoor photography that involves naturally occurring subjects.
These can include:
Wildlife is definitely one of the toughest photography subjects. You have to deal with moving, unpredictable subjects, long focal lengths and often lighting which is out of your control. In contrast to a portrait in a studio which can be easily controlled, you generally have no control over anything when taking pictures of wildlife in their natural habitat. The only thing you can control is your camera and lens!
Taking pictures of water such as oceans, waterfalls and lakes can be benefited by using a polarizing lens which takes away some of that glare that we so often see with water photos. You'll notice a big difference when using a polarizer.
If you enjoy taking photographs of insects then consider a macro capable camera or even better, an SLR camera with a macro lens. The macro photography section of this site covers this topic in more detail but macro photography in the outdoors is definitely a type of nature photography.
Nature and wildlife photography are extremely rewarding forms of photography and one that every photographer should experiment with.