What is ICS? More cities is definitely beter in Civ III, you don't get a penalty for adding another city in Civ III, in both successors you do, so I understand what you've heard about it. Civ III has a corruption system that is meant to prevent you from sprawling all over the place, but it doesn't really stop you. However, if you're afraid Civ III is just about cranking out the highest amount of cities in the shortest amouint of time, then no, it's not quite like that.
Okay, part of it is, otherwise players wouldn't go on and on about the maths of settler farms. Most high level players are judging a start by its ability to produce settlers efficiently, that's true.
But you get most out of the game if you're building stuff as well, and for that, fewer, bigger cities are better.
If, for example, you want to build spaceship parts, it's more efficient to do that in big towns with an excellent production than in a small town that had to remain small because you've put so many other towns right next to it.
What you'll see in Civ III is that many players will leave their core cities with plenty of space for building stuff, but in remote regions, where the corruption is very high, ICS rules. Nobody will argue against ICS in completely corrupt regions... unless perhaps you've chosen Communism as your goverment, as it has a flat corruption system, that's different.
Civ III is not a lesser version from its successors. It has tech trading, map trading, contact trading, real trade networks, reputation, espionage, embargo's, war weariness, alliances, and those are all things that are lacking in Civ 5. With Civilization every new game has seen the developers throwing systems overboard and replacing them with new ones. It depends a lot on individual taste which version you like better.