What is the formal charge on the nitrogen atom in ${\mathrm{HNO}}_3$ ?

 

The appropriate Lewis structure is $\mathrm{H}-\mathrm{O}-{\mathrm{N}}^{+}(=\mathrm{O}){\mathrm{O}}^{-}$

The nitrogen atom is quaternized and has a formal positive charge, whereas one of the oxygen atoms has a formal negative charge. Of course, the Lewis structure represents the molecule's neutrality.
Keep in mind that nitric acid dissociates when:

${\mathrm{HNO}}_3\text{ (aq) }+{\mathrm{H}}_2\mathrm{O}\left(\mathrm{l}\right)\to {\mathrm{H}}_3{\mathrm{O}}^{+}+{\mathrm{NO}}_3^{-}$

There are 3 formal charges on the nitrate ion 

${ }^{-}\mathrm{O}-{\mathrm{N}}^{+}(=\mathrm{O})-{\mathrm{O}}^{-}$

Although the anion is again formal charge separated in our depiction, the total charge on the ion is still 1.