Well, for starters, it's an immense game in it's scope yet it fits on just two floppy discs. It has basically unlimited replay value and an enormous amount of very cleverly and tightly presented information about the game itself, and history, available at the click of a button, at any time you want. And it is yet so simple to play and "get into" that all of the complexity behind the blocky sprites seems to fade away as you're playing.
It is also astounding how real a model of our little planet, and our geologically insignificant species this game is. There are just too many analogies to real world events that you can can clearly see in it. And they're not limited only to historic events, the workings of the game also do a very decent job of representing how the world works in general. It's an educational, thought-provoking AND fun game, and everything in it, including it's space age (for 1991) AI, is held together by relatively simple mathematics. It's basically as good as games get and by far the best in its genre.
Yet Civilizatrion is imperfect, and that is probably its most appealing quality. Many people including Sid Meier have tried to make it better but none have really succeeded. The lack of "realism" in Civ, like the famous phalanx that sits on a beach for 3000 years and then sinks a battleship or shoots down a bomber, is what makes this game more fun than the rest of the bunch. It's these little shocks the player experiences, the ways things go wrong when they shouldn't, that keep you on your toes and help you learn the game.
And when you get decent at it, addiction kicks in. The "one more turn" phenomenon in Civ has been very thoroughly documented. I think I am already starting to repeat myself - Civilization is as good as games get. And then some.