Yep. I tend to sleep on my arms, so it happens a couple of times a year. I've been freaked out by it, too, when it sometimes takes longer than expected to regain feeling. It can be eerie.
I am marveling that someone can reach the age of 20 and never have heard of a limb falling asleep.
Try sleeping on your arm all night. Then complain lol.
It's a compression of the radial nerve (less often the median or ulnar nerves) caused by the position. Severe cases (brought on from trauma or prolonged compression) result in radial peripheral neuropathy, also known as "Saturday Night Palsy" which can be more serious.
I once woke up, and sat up, and somehow pulled my neck pretty badly. Sleep can cause injuries a lot of the time.