Is the concentration of negative ions always equal to that of positive ions?

Is there any way in which a solution can have more negative charge than positive charge, or vice versa? For example, in the context of acid-base chemistry, is there any scenario in which $[\ce{H+}]\ne[\ce{A-}]$? I have never heard of a solution with a non-neutral overall charge, but is it possible in some extreme scenario?

• Well, a trivial and unhelpful answer would be to consider a solution of $\ce{MgCl2}$: there are twice as many negative ions as there are positive ions. A solution that is electrically neutral does not necessarily have the same number of negative ions and positive ions. – orthocresol May 27 '16 at 19:39
• You're right, of course. Question edited to say charge, not ions. – Marcel May 28 '16 at 16:28

The only point that $[\ce{H+}]=[\ce{A-}]$ is when the $\mathrm{pH}=\mathrm{p}K_\mathrm{a}$ of a given acid, so indeed in most instances $[\ce{H+}] \neq [\ce{A-}]$. In addition to $\ce{A-}$, the solution also contains negatively charged $\ce{OH-}$ that balances the positive charge of the $\ce{H+}$ ions. If the acid is titrated with a strong base (e.g. $\ce{NaOH}$), the positively charged $\ce{Na+}$ ions balance the negative charge of $\ce{OH-}$ and $\ce{A-}$.