The game has three major and two minor attractions for me.
The story element appeals to me, like books, comics or movies. The evocative nature of the game is a heady and consistent draw.
The active nature of the game is important, like video games or sports (or really, any games). The particpants make a difference, and create the outcome together.
The social nature of the game is probably paramount for me. It's like a team sport or poker night. My group probably spends nearly as much time socializing as playing. The cooperative, instead of competitive, nature of the game also makes the atmosphere more relaxed, friendly and fun. We laugh. Often.
The progressive nature of the game. Monopoly starts every game at the same state. In D&D characters gain power, history, allies, enemies. Find a magic sword at the end of one game, and you start the next game with a magic sword. The game and characters evolve to keep the challenges fresh and fun.
Related to the story element, is that parts of the game can be reused. NPCs recur as often as necessary. Favorite villians keep coming back. Allies, henchmen, sidekicks, rivals, comic relief NPCs; they're all awaiting another call to the stage.
I could go on (seemingly) endlessly on the points above. I have a complete essay somewhere, but those above are the major points.
-Dave