Step 1: Understand cell motility.
Motility refers to the ability of a cell to move or propel itself. Among human cells, motility is primarily observed in sperm cells, which move through the reproductive system to fertilize an egg.
Step 2: Review the options.
- Nerve cells are not motile; they transmit signals but do not move.
- Cutaneous cells are skin cells and do not exhibit motility.
- Egg cells are large and immobile, relying on sperm for fertilization.
- Sperm cells are the only motile cells in the human body, using their tail (flagellum) to swim.
Step 3: Conclude.
Sperm cells are motile, making option (D) the correct answer.
Final Answer:
\[
\boxed{\text{Sperm cell}}
\]