The first two are classics, with Diablo II being on my top five games of all time list. Sunk so many hours into that game it's not even funny.
Yup, this is why the first two are on my "to play" list. 
Oh. PS4 might have the same. I'm not really sure because I'm always connected to the internet - unless my internet decides to sh*t itself. I'm not really keen on online always though. If my internet does muck up, I still want to be able to enjoy the game I purchased.
This is precisely why I'm never buying Diablo 3. If I pay for a game that is not a MMO, or that has a single player campaign, I want to be able to play it even if I'm not connected online.