Two examples I've seen of this so far are in statistical mechanics, when looking at the work done on a system:
$$dW=-\frac{1}{\beta}\frac{\partial \ln{Z}}{\partial V}\delta V$$
and in the Noether charge:
$$Q(t)\equiv \frac{\partial L}{\partial q'_{i}}\delta q_{i}$$
Why use the $\delta$ and not just $dV$ and $dq_{i}$?
