My A500 (and later my A1200) was connected to the internet as far back as 1990 thanks to the university I was attending at the time. Downloaded a lot of Amiga games that way (I was a poor college kid at the time so don't hurt me).
Other than that I used it for the usual...creating music, playing games, writing papers. My roommate and I would play Lemmings and drink beer all night long. Good times.