Flash photography has been looked down by some proclaimed “experts” as a lower form of photography. In fact, these same people instruct beginners to always shoot without the flash, if possible.
In the case of point–and–shoot compact digitals, shooting without the flash can give you better results, but not all the time. Backlit scenes are almost always better shot with a flash. For indoor shooting, it boils down to choosing between blurred no–flash photos, or bad flash photos. Using a flash can make or break a photo.
SLR shooters on the other hand have the luxury of using hotshoe flashes for creative lighting. However, you really have to understand your flash system to make the most out of it. Canon users would benefit much from this photonotes.org article on the EOS flash system.
After learning the technical aspects of flash photography, improve on your skills by learning its practical applications, including the technique involved. To get an idea how certain lighting effects are achieved through the use of a flash, dg28’s technique page should get you running. For more on flash photography and creative lighting, the Strobist blog is a worthwhile regular read.