There are only two kinds of charge interaction - attraction and repulsion. This can be easily shown using axial symmetry of a system of two interacting point charges. You might be greatly surprised, but this fact itself does not mean that there are only two kinds of charges in the universe - "positive" and "negative". Let me give an illustration:
Imagine you set an experiment where you explore point charge interactions. Get a bin and put the first charge there. The second charge repels the first, put it to the same bin. The third one attracts the first two charges, it's a different kind of interaction, so it cannot be put to this bin. Take a second bin and put the charge there. Some time later we'll have two bins, each containing charges repelling each other and every charge from the first bin attracts to every charge from the second bin. Looks very usual, isn't it?
These are our well known charges named "positive" and "negative". But now we take the next charge from the environment with very interesting properties: it attracts to every charge from both bins. It cannot be put in either existing bin since it's demonstrating a different kind of interaction with charges in boths bins. Now we have nothing to do but to take a third bin for this charge. Also we have to choose a name for the new kind of charges, let it be "asterisk".
If we go on with collecting charges, finaly we'll end up with three bins, each containing charges repelling each other and every charge from either bin attracts to every charge from another one.
During the whole human history people have seen only charges that perfectly fit into only two bins, this is why we have only positive and negative charges nowadays. But nobody can state that a third kind of charges will not be discovered in the future. An existing theory in physics must describe all experiments ond observations performed. But think, if such discovery is made, we'll have to deny the future or just invent a new theory?
ElectroMaster88 said:
It just seems impossible because an electrical charge can be measured in numbers, and numbers can be just positive, neutral or negative.
No, the logic here is right opposite. We are able to represent charges as scalar algebraic values because we have only two kinds of charges, not vice versa. If there were more than two kinds, physicists would employ another way to mathematically express them.