I will start off by saying that I am not really a "goldfish person" and have not kept them in a longgg time... I keep tropical fish now exclusively, as goldfish tend to need a good amount of room (explained below). This species does really deserve a few words of mention, however, due to their popularity.
Goldfish are the oldest ornamental fish kept by man as a pet, originating in China as a descendant of the wild carp (as a result of these genetic roots, they are a cold-water species prefering temps in the mid-60's, rather than high 70's, unlike just about every other fish mentioned on this site). Since then, they have been bred into a huge number of color and shape varieties, but all are still considered the same species. In pet stores, you will see a lot of this variety, ranging from the plain torpedo-shaped "common goldfish" sold as feeders and given away as carnival prizes,
all the way to the unusual fancy forms--black moors, ryunkins, bubble-eyes, lionheads, oranda, calico, etc.
They really are beautiful animals, but I'm saddened to see that so many are kept in what amounts to rather appalling conditions. Just to give a bit of the article away, it is mostly due to their great quantities of waste production, which can lead to stunting and disease in a smaller container. These are fish that grow very big (some up to a foot) and very old (several decades) if given the chance in a decent-sized tank or pond.
Many are surprised to find out that the supposedly-healthy fish they've had in a bowl for a long time is actually only 1/3 of its expected natural size for that age. This sort stunting is more than just a matter of "growing to the size of the container", but stunting is the result of stress that also impairs the immune system and in the long term can predispose to disease and premature death.
Goldfish are omnivorous and do well on a variety of foods, but when fed too much protein and not enough fiber, can get a blockage that results in swim bladder problems.
The squat/round "fancy" types are most susceptible due to their body shape.