Without Internet (well, without a connection to it) I'm losing roughly 80% of my PC games library (or rather, access to it). The rest are my retail games I have, but that's not all, even if I do have retail games to play off-line in case I do not have access to Internet then I am stuck to play pretty much all of them non-updated, since the patches for them are on the Internet and just so happens not to all be backed-up on physical discs (which I did, but not for all of them).
Internet is "required" for a lot of things, I don't see it being bad that D3 requires such a thing to be able to play it. And honestly, who would want to play D3 off-line? For Diablo 1 and 2 I can understand, of course, but Diablo 3's game-play mechanics and features pretty much rely on dynamics, live stuff happening as the players make it happen (dynamic economy, friends, contacts, games creation, arena, planned matches, co-operation, etc), it wouldn't be much interesting playing it off-line unless someone just wants to learn about the story through a single play-through and then call it a night. But then that's not playing Diablo 3, that's merely following a story that can be watched on YouTube after the game is released, and such a person would save money by doing that rather than buying the game to find out what happened to Tyreal.
I just don't mind at all.