Mine is from back in the dawn of the internet (around 1997 or 98, IIRC.)
So, in an old site called Neopets, I got my account banned for making it to the top of the high-score table in several games in one day - I guess the actual trigger was that the three daily tries at the Snake clone were in the high-score list. In short, the site's admins thought that being good at their built-in minigames was "hacking."
And they were pretty much "no refunds" about it, too.
Banned for not being a scrub, I guess? >_>