I often carry my 600mm lens on the photo walks I lead at Cape May Point SP, NJ. This invariably leads some to ask if they need big, heavy, expensive gear to photograph wildlife. The good news is no, so long as they select subjects appropriate for their equipment.
Fortunately, there are such subjects: butterflies, damselflies, and dragonflies, among others.
My first digital camera was a 5 megapixel point-and-shoot which, in July 2002, I took into central Mexico where I photographed a Dingy Purplewing, Four-spotted Sailor, Montezuma Cattleheart, and Walker's Metalmark. Later that month, I participated in a July butterfly count in Mission, TX, where I shot a Gray Cracker and Malachite with the same camera.
The trick to creating good images of such subjects is to get close and to have your subject parallel to your camera's sensor plane.
Today, a very good point-and-shot camera can be purchased for under $500.00, and are of much better quality than those of a decade ago. In other words, for relatively little money (at least in terms of photography) you too can buy the equipment needed to become a wildlife photographer. Obviously, you will still need to learn how best to use your equipment, but that's part of the fun of being a wildlife photographer.
Finally, not all of the images surrounding this brief article where shot with point-and-shot cameras, but all of the could have been.