Diablo is a single-player game first and foremost. You don't ever have to touch online if you don't want, and you can still enjoy it greatly. If you hate playing games online, do not let that talk you out of playing Diablo, really.
I like playing online though. It's fun to take on a huge bad guy with a group of guys and topple him, then go crazy trying to scrounge on the ground for PHAT LOOTZ before anyone else picks it up.
Plus, it's easier to get the rarest stuff by trading than finding it all. And you can PVP online. If you want.