One of the best the turn-based strategy genre has produced.
Civ III is neither of the above, having just the right amount of pace for players - and in fact, there are many paces. With around seven levels of difficulty, from the easiest Chieftain, to the hardest level (cheekily named "Sid", after the chief designer of the game Sid Meier), there is always a level just right for any aptitude of player.
Civ III is not an easy game. Being a middlingly lousy player at games, I found myself in a rut in the third easiest difficulty level after having played a few games. It being turn-based, every turn counts. If you waste a turn at the start, you may regret it going into the end of the game as other civs improve and progress more than you.
What impressed me about the game was the sheer variety of everything, including the ways of winning. In Civ III, you could win by a number of ways: technology (sending a spaceship to the moon), conquest (the original way of winning), culture (being so rich in culture that other civs simply pale beside you), and many more - just like in real life. Also, there is a large number of civs for you to choose from, each with their own beneficial characteristics. Therefore, you may want to choose a civ that aids in your gameplan. Personally, I like to be ahead in technology, and thus pick a Scientific civ, like Germany.
There are many technical aspects of the game which I can't even start to name (I am not a very good game player and computer user). Civ III may not appeal to many people, like those who abhor the very idea of turns, or ancient civilizations. However, for other game players, you cannot miss out on Civ III.
(I advise that you get Civ III: Complete, which comes with Civ III's two expansions: Play the World [multiplayer mode] and Conquests [a handful of preset scenarios that you can play, including Mesopotamia and World War II - they even come with tech trees different from the standard game, thus making it more fun!)