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Ok. So I have 4 Fish, all of different breeds. A Fantail(of which kind I am not sure. He is thin bodied but beautiful with a long flowing tail), A Common Goldfish, An Ogon Platinum Koi, and a Butterfly Koi. I would like to breed this spring but I am not sure if I can cross breed. So, I am asking for some information. Any tips or knowledge would be nice! Thank you.
Jordan

its fine to cross breed fish. they will have varying levels of each parent in them and different shapes. for example, one of my fry is a canary yellow goldie/sarasa comet which looks just like the daddy, the yellow one but has a deformed mouth. also, i have 4 pearlscale/moors. 3 of them are slender like the moor and the other one is like a little golfball like her mummy. you can also cross single and double tail fish. i have a pearlscale/shubunkin that turned out great! in closing, all breeds of fish are made from the deformities of the common goldfish so breeding them back shouldnt be a problem although i dont think id recommend breeding the koi with the fantail as the fantail may get a little beaten up. double tails are slower than single tails and koi are stronger fish than the average single tail so id avoid that. anyway, sorry to waffle on a bit. just thought youd like a bit of 'history of the goldfish'.
sorry this post was overlooked for so long! good luck!

koi and goldfish are different species.
So they can't breed, it would be like breeding a dog with a cat.

Not according to the thread down below:

Can Koi and Goldfish Breed?

There's a link there to a picture of the result which looks like a great big coloured carp. They think they may be sterile tho... like a mule.

Goldfish (and koi too, for that matter) do not breed true and you will always get a variety of shapes and colors. The desirable traits are all polymorphic. The desirable traits are either recessive or have incomplete penetration of dominance. The percentage of culls can be quite large and the percentage of really excellent fish is always very small.

Thus, breeding goldfish is a numbers game. The object of the game is to get the maximum number of good-looking, true-to-type fish with the minimal amount of space and effort. If you pair different varieties, you are playing the game with one hand tied behind your back.

Generally, you will maximize the percentge of good-looking, true-to-type fish by line breeding (crossing siblings, cousins, etcetera). If the line becomes "weak" (e.g. there is an unacceptable percentage of deformities, fish which cannot carry their tail, etcetera) then you need to out-cross by pairing fish from different genetic lines. When out-crossing, you want to pair fish which are genetically different enough to generate some inter-varietal hybrid vigor, but not so distant that the percentage of good-looking and true-to-type fish becomes unacceptably low.

By pairing completely different varieties, you are carrying out-crossing to the extreme. The offspring will be strong, but very few will look like either of the parents. You get very few good-looking, true-to-type fish for the space and effort devoted to the task.

I am with you there, Bekko - I'd rather breed my fish within the same breed. There are already plenty of mutts all over the place in pet stores, and the true meaning of breeding is to keep the true breeds alive, not criss cross them and get all kind of undesirable fish out of it.

Now, accidents in breeding do happen, and crosses come out. My first breeding effort ever was the cross of an oranda with a telescope, and I gotta tell you, as cute and lovely as the fish were, hardly one assembled either an oranda or a telescope.
I have my fish outside all breed oriented in their own tubs now, no more mixing and matching - ryukin with ryukin, oranda with oranda, ranchu with ranchu, wakin with wakin. Once in a while breeders have to bring in a different breed to keep the desired strain strong, but other than that, no mixing.

One last thing to say is that the hybrid is a sterile breed too and you wouldn't find it in true nature