What are some other examples of koans?

Mumon's "The Gateless Gate":

Mu (Nothingness): A monk asked Master Zhaozhou, "Does a dog have Buddha nature?" Zhaozhou replied, "Mu" (which means "no" or "nothingness").
"The Sound of One Hand Clapping":

A famous koan from the Hakuin School of Zen that simply asks, "What is the sound of one hand clapping?"
"What was your original face before you were born?":

This koan invites the practitioner to reflect on their true nature, beyond birth and death.
"When both hands are clapped a sound is produced; listen to the sound of one hand clapping.":

Another version of the one-hand clapping koan, often attributed to Zen Master Hakuin.
"A monk asked Master Yunmen, 'What is Buddha?' Yunmen replied, 'A dried shit stick.'":

This koan challenges preconceived notions of sacredness and the idea of Buddha as something pure or holy.
"Out of nowhere, the mind comes forth.":