When to exercise American calls and puts early

On a stock that pays no dividends, can it ever be optimal to exercise an American call before expiry? What about an American put?

Never for the call; sometimes for the put. The call is worth at least $S-Ke^{-r\tau}>S-K$, so selling beats exercising, and exercise also gives up the insurance value. A deep in-the-money put can be worth exercising because receiving $K$ now earns interest, which can outweigh the small remaining optionality when $S$ is close to zero.