So, there are many different types of goldfish.
Some are cute, and some are not as cute, and some are just plain ugly. (no offence to those who like the fish that I consider not as cute or ugly.)
Most of them can be black, white, red, orange, yellow, or any combination of those colors.
Common
The common goldfish is usually a feeder fish. Sold in a tiny tank, mixed with comets sometimes. (Note: I couldn't find a nice picture of a healthy common goldfish...)
Comet
Sometimes a feeder fish, looks a lot like common goldfish but with a longer tail. Rory is a comet.
Oranda
A medium fish with a wen (big raspberry thing) on its head. Can be any combination of colors, but red and white is the most famous.
Celestial
The goldfish was bred to be looked at from the top, and so the celestial goldfish looks up at you. Its tank shouldn't have much in it besides it, because it can't see as well as other goldfish.
Bubble-Eye
Bubble-Eye goldfish have big, fluid-filled sacs underneath their eyes. They have no dorsal fin, and are a little slow, so don't keep them in a tank with speedy goldfish.
Pearlscale
Pearlscale Goldfish are fat-ish fish with little pearly bumps on their scales.
Fantail
Fantail goldfish have extra-long, super-flowy double tails.
Moor
Is one of the most debated goldfish out there. Some say that it is only a moor if it is all black, others disagree...
Wild coloring
The wild coloring of a goldfish is this sorta bronzy-green.
All pictures were taken from Google Image. If one of your images is on this site, I'm sorry for not giving you credit.