Korea about 1400AD
http://en.wikipedia.org/wiki/Hwacha (http://en.wikipedia.org/wiki/Hwacha)
Rocket launched arrows. Anyone know of something earlier?
That's what I immediately thought of when I read your thread title.
I've been playing Civ IV a lot recently, so yeah, the same thought occurred to me too!
Mythbusters built one. One of their cooler builds IMHO: http://www.youtube.com/watch?v=jeQTpmaEkMY