Wage regressions: Nominal versus real wage
Because you want to measure the real impact of education.

If there is inflation, the nominal wages most likely will go up over time, but you don't want to think that your return to education does that, it's just inflation.

If, on the other hand, you're comparing wage differentials, say $\log w_s - \log w_u$, where $s$ indicates skill and $u$ indicates unskilled, you do not need to correct for the price level.

To see, note that

$$
\log w^s_t - \log w^u_t = \log \frac{w^s_t}{w^u_t} \\
\frac{w^s_t}{w^u_t} = \frac{\frac{w^s_t}{p_t}}{\frac{w^s_t}{p_t}}
$$