I remember burning CD's full of 1 minute songs that never completed because someone was always calling our house line, disrupting the internet connection (and there were no resumable downloads). Good times ;)
By the p2p era (which napster was) they absolutely needed to do resumable downloads because a peer could suddenly go offline.
Before that I remember getting mp3s from ftp and irc fserves... Ftp definitely had resume, though not all clients and servers did it.