Although Goldfish, the most popular type of coldwater fish, originated from Japan and nearby regions many strains have been developed by captive breeding around the world so many of the details below are rather vague. This is especially true of the size and origin of the fish. I have listed the more popular types of Goldfish as well as other breeds to help you decide which would suit your needs.
Species Name: Acanthorhodeus atranalis
Origin: E Asian streams & lakes
Size: 8cm
Temperament: Peaceful
Food: All cold water aquarium food
Tank Areas: Middle & bottom
Notes: Quite colourful for a cold water fish with a pink body and slightly yellow caudal fin. Many new colours are being bred into the fish by experts in Japan in a similar way to Koi.
BLACK MOOR: 
Species Name: Carassius auratus
Origin: Captive bred
Size: 12cm
Temperament: Peaceful
Food: All coldwater food
Tank Areas: All
Notes: Like all "Goldfish" this fish is very difficult to sex. Seems to like the company of other fish. Can be bred but adults should be removed after spawning. Not suitable for outside ponds as it's fins are easily damaged by very cold water
BUBBLE-EYE: 
Species Name: Carassius auratus
Origin: Captive bred
Size: 12cm
Temperament: Peaceful
Food: All coldwater food
Tank Areas: All
Notes: Am I the only person that thinks that this is fishkeeping gone mad. Why breed a fish that is so prone to damage. If you must have them, keep them away from other fish and don't have any sharp ornaments in the tank. Better still don't keep them at all.
CHINESE SAILFIN SUCKER: Picture Required
Species Name: Myxocyprinus asiatica sinensis
Origin: E. Asian lakes
Size: 30cm
Temperament: Peaceful shoaling
Food: All coldwater food
Tank Areas: Bottom
Notes: Odd looking fish with a very high triangular dorsal fin. Often kept with tropical fish but seems to prefer a cold water tank. Not suitable for outside ponds though.
COMET GOLDFISH: Picture Required
Species Name: Carassius auratus
Origin: Captive bred
Size: 20cm
Temperament: Peaceful
Food: All coldwater food
Tank Areas: All
Notes: This fish needs lots of space to flourish. Best kept in a large outside pond or a very large tank
COMMON GOLDFISH: Picture Required
Species Name: Carassius auratus
Origin: Captive bred
Size: Variable
Temperament: Peaceful
Food: All coldwater food food
Tank Areas: All
Notes: Probably the most popular fish in the world for fishkeeping. Needs a quite large tank or can be kept year round in an outside pond. Females are usually plumper and males get white spots on their gills when spawning.
Species Name: Carassius auratus
Origin: Captive bred
Size: 20cm
Temperament: Peaceful
Food: All coldwater food
Tank Areas: All
Notes: A lovely fish that can be kept in a tank or outdoors in a pond (try to prevent freezing though)
Species Name: Cyprinus carpio
Origin: Captive bred
Size: Variable
Temperament: Peaceful
Food: All coldwater food
Tank Areas: Pond only
Notes: Koi can grow very large and need good filtration as they produce a lot of waste. Should only be kept in a large pond.
LIONHEAD GOLDFISH: Picture Required
Species Name: Carassius auratus
Origin: Captive bred
Size: 15cm
Temperament: Peaceful shoaling
Food: All coldwater food
Tank Areas: All
Notes: This fish is unlikely to survive in a pond. Needs a peaceful environment to thrive.
Species Name: Carassius auratus
Origin: Captive bred
Size: 12cm
Temperament: Peaceful
Food: All coldwater food
Tank Areas: All
Notes: As with it's red capped cousin, this fish should be kept indoors and away from over zealous tank mates.
ORANGE SPOTTED SUNFISH: Picture Required
Species Name: Lepomis humilis
Origin: USA lakes & streams
Size: 10cm
Temperament: Peaceful, shoaling
Food: Carnivore food
Tank Areas: Middle & bottom
Notes: One of the smaller members of the Sunfish family and as such, easier to keep in the aquarium. During mating the male grunts to attract the female's attention. The spots on the female tend to be less orange and more of a brown colour.
Species Name: Carassius auratus
Origin: Captive bred
Size: 12cm
Temperament: Peaceful
Food: All coldwater food
Tank Areas: All
Notes: These "fancy" goldfish are not very good swimmers and should only be kept in tanks.
PUMPKINSEED: Picture Required
Species Name: Lepomis gibbosus
Origin: USA lakes & streams
Size: 22cm
Temperament: Mainly peaceful, shoaling
Food: Carnivore food
Tank Areas: Middle & bottom
Notes: A member of the Sunfish family. Quite colourful with iridescent blue spots covering it's brown skin. During spawning the male digs a pit in which the female deposits the eggs. Best kept in groups which requires a very large tank.
Species Name: Carassius auratus
Origin: Captive bred
Size: 20cm
Temperament: Peaceful shoaling
Food: All coldwater food
Tank Areas: All
Notes: Should only be kept indoors in a large tank. Do not keep this fish with very active or agressive tankmates.
RUDD: Picture Required
Species Name: Scardinius erythrophthalmus
Origin: Central Europe and UK rivers and streams
Size: 20cm
Temperament: Peaceful shoaling
Food: All coldwater food plus live food
Tank Areas: All
Notes: Can grow quite large so a big tank is required. Only easy to sex during spawning when the males develop tubercles on their snout. Should only be kept in groups.
Species Name: Carassius auratus
Origin: Captive bred
Size: 20cm
Temperament: Peaceful shoaling
Food: All coldwater food
Tank Areas: All
Notes: My favourite goldfish, peaceful and active. Quite easy to breed but the parents and other adult fish should be removed after spawning.
THREE SPINED STICKLEBACK: Picture Required
Species Name: Gasterosteus aculeatus
Origin: European lakes and streams
Size: 8cm
Temperament: Mainly peaceful
Food: Live food only
Tank Areas: Middle & bottom
Notes: Not particularly good as a aquarium fish as they don't like many prepared foods. This active fish is easy to sex when spawning as the males head turns red.
Species Name: Misgurnus anguillicaudatus
Origin: E. Asian streams
Size: 10cm
Temperament: Peaceful
Food: All aquarium food
Tank Areas: Bottom
Notes: An easy to keep fish that can be kept in a slightly heated (65 F) cold water tank or a cool tropical one. Gets quite lively when barometric pressure is low.