For me - being around since WAY before the beginning (we are talking years of devouring every detail about the development of D3)..
The thing I love the most is the "redemption" process that the game has undergone. Really, starting with RoS
I have never been more excited for a video game than I was for Diablo 3. And after about 1 year of denial after the launch of Vanilla, I gave up on it.
But Blizzard proved to be up to the task and its the single thing about this game that makes me love it so much nowadays. Blizzard took what was an AMAZING shell of a game and has turned it into an amazing game. They FIXED Diablo 3. So proud of them for being willing to shut down the Auction house. The free updates since RoS launch with so much content each time - its amazing!
When I play Diablo 3 now, I get the same warm, fuzzy feeling that I had back in the day playing Lord of Destruction. Only its even better because we've seen the progress they've made since May 2012. 3 1/2 years and they've turned the game into something awesome - can't wait for more expansions!