I bumped into this short video a while back of a very cute kitten suddenly being overcome by sleep, along her "dad's" arm:

Someone else (forgive me for forgetting who) pointed me to the blog Cute Things Falling Asleep, which definitely lives up to its name!  Featuring mostly baby animals suddenly snoozing, there are a few older animals and some babies and children catching the bug as well.  Here are a few especially cute samples: