One of the best strategy games of all time.
Civ 3 still has the most pleasing graphics of any game in the series. Units are nicely animated, and the world is well represented, always giving you a clear picture of what is happening. I am a self confessed fan of isometric graphics (I'm of that age), and are something in my opinion the gaming industry has abandoned all too readily.
The interface however, although slick and well designed has its flaws - some buttons on the main screen are small and poorly placed - you can easily intend to activate the diplomacy shortcut only to mouse-slip and accidentally end the turn. Also in the diplomacy screen not all of the rival leaders can be viewed at once. On larger games chopping and changing which leaders you are viewing can make it difficult to keep up with changing attitudes and the state of international relations.
The AI, although tough like in all Civ games, can lack subtlty at times and is noticeably crude. Barbarians do not work at all, only attacking when a unit is on a certain axis, and the persistent problem of the AI not knowing how to use sea units or navies effectively remains. Although the AI normally has a healthy (cheaty) advantage in technologies and manpower, it can be easily out thought and manipulated by a cunning player. That being said the AI will always offer a good fight, and should not be underestimated.
Diplomacy is improved greatly from Civ 2 but remains flawed. Getting the optimum deal from negotiations is a time consuming affair, with an unhelpful adviser leaving no choice but to constantly tinker with proposals until the most favorable arrangement can be figured out. On the whole though, leaders cannot be as easily manipulated as in past games, they know when is a good and bad time for a fight, and often make good use of alliances with other AI.
Civ 3 also has some excellent total conversion mods - Medieval Europe Mod II, The Ancient Mediterranean are must-plays, and there is always a reason to play again. The game is easily edited, as it comes with a useful editing application. This allows you to tailor the game just so, giving boundless replay-ability.
The bottom line is I payed ~£30 for this in 2001 and I'm still playing it. It's a great game. If you like Civ, 4x or strategy games, get this.