Is the concentration of negative ions always equal to that of positive ions?
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 $\ce{A-}$.

To answer the question in your title though, yes, charges are always balanced. To quote another good post on this topic: 


  While it is true that solutions are not always locally electroneutral, that non-neutrality is small, and does not extend to larger scale. Thus, it does not impact chemical concentrations: you cannot separate positive and negative charges in a solution at a macroscopic level.