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I know that a salt is the product of a reaction between a base and an acid, but does this mean that there will always be one cation and one anion and therefore a neutral charge?

In relation, are acids and bases charged?

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    $\begingroup$ IUPAC defines salt as "a chemical compound consisting of an assembly of cations and anions", so virtually there is no limitation on whether it can be charged or not. $\endgroup$ – andselisk Jul 29 '17 at 6:26
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A salt is an ionic solid compound. As such, it needs to have a zero net charge.

However, that doesn't mean it should contain only one cation and one anion. The stoichiometry of the salt depends on the charges of the ions. For instance, iron (III) sulfate is $\ce{Fe2(SO4)3}$; this stoichiometry is required to balance the charges from $\ce{Fe^3+}$ and $\ce{SO4^2-}$.

Also, other types of salt exist, called mixed salts. They contain several different cations and/or anions (e. g. $\ce{KAl(SO4)2}$).

Compounds with a net charge exist, they are just not called salts (look up Complexes).

In relation, are acids and bases charged?

Acids may (e. g. $\ce{NH4+}$) or may not (e. g. $\ce{H2SO4}$) be charged. Similarly, bases may (e. g. $\ce{SO4^2-}$) or may not (e. g. $\ce{NH3}$) be charged.

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