Control theory: is there any actual application for D in ABCD matrix?
A lag-lead compensator in state-space form will have non-zero \$D\$. 

In \$H_2\$ or \$H_{\infty}\$ control design if the performance variables include the input (e.g. keep it 'small') then again \$D\$ will be non-zero.

They can also appear when a continuous-time system is approximated as a discrete-time system (e.g. convert \$\frac{1}{s+p}\$ using Tustin's transform).