I remember when I first played Diablo. It was an experience I couldn't liken to anything else. The simplicity of the interface combined with the depth of character customization and powers made for long hours sitting and staring at a CRT monitor. Is it any surprise that the series is still going strong (a lot of people still play Diablo II) and with a third game on the way, players are salivating at the chance to return to Sanctuary. When multiplayer hit Diablo, the game significantly improved. Slaying monsters, looting treasure, and general banter with your friends made the experience much more fulfilling and incredibly social.
Diablo has had a lot of staying power because every time you played, you would have a different experience. Random dungeon generation combined with hundreds of item combinations always made for interesting trips into the deep, dark holes of the earth. Diablo II added runes and sockets, which increased the item customization and added a great deal of depth to the game. Additionally, seven classes were ultimately added, and each had capabilities to use different item sets. And who could forget the horrible, yet amazing, "Hardcore" mode? A relatively new thing in RPG games that added a twist to the "risk/reward" formula.
What made Diablo great for me is its simplicity. It was accessible to more casual gamers, but could offer an intense and hardcore experience as well.
Hats off to Blizzard for creating one of the most addictive franchises of all time.