Let me tell you something, piranhas are not your average neon tetra. They have one thing in mind, and that is food; and whatever that moves is a potential meal to piranhas.
With that said, there are two main genera of piranhas commonly kept in home aquariums - Pygocentrus and Serrasalmus.
Now, we all know that all species within the Pygocentrus genus are schooling fish and can live amongst each other. But here's where it gets tricky, because every once in a while, you'll come home to find a fish or two that is killed and eaten within a school of piranhas. This goes to tell you, that even schooling piranhas will attack each other and the weakest/injured fish will be taken cared of by cannibalism. So the idea that you would like to house your favorite cichlid in with these toothy ]\/[onsters should be off the table, unless you install a divider.
On to the next genus, and this is the Serrasalmus. Now, even though they're often considered solitary animals, many actually does form loose schools in the wild, but that requires an exceptionally large tank if you would like to duplicate that in your aquarium, and the chances of you succeed in doing so is very very very very very very very very very very ..... slim. If you don't want a fish with missing fins or missing body parts or worse yet, in-half, then you should keep them alone, doesn't get any more complicated than that.
You may say, "Well I've heard of *such and such fish** being kept successfully with piranhas." Well, like all things in life, there are exceptions to the rules. But that doesn't mean it'll work out for everyone in every situation for every fish. One person may be able to keep a pleco with his school of red bellied piranhas, but that doesn't mean your school of red bellied piranhas won't tear the same fish apart and have it for dinner. You get my flow??
In short, if you can't deal with the fact that these are fish to be kept by themselves, then don't get piranhas.