Maybe it's because it was the first one I played, but something about the 2d aspect of this game gripped me. I don't have the same love for the games that came after it, the 3d graphics somehow take me out of the historical element.
The fact that in the older games you are basically playing on a map, gives off this almost board-game feeling that is cosy and immersive. (I know that civ was inspired by a board game)
Playing civ3 as a kid really made me feel like I was in whatever era I was playing at. Still remember those jazz fusion tracks especially.
I remember seeing resources on the map, hating how arbitrary they felt, and then grew to love macemen as midgame doomstacks that justified any war for iron in the early game.
Civ3 helped me understand and justify my early wars for any nation, not just the Mongols and Zulu.