Let's discuss the rules that govern the civ3 AI.
1) Trading: civs negotiate for what would benefit them and their civ. If it's not worth it to them they won't trade. They always look for some benefit so if you want one tech, in later stages of the game the AI may want 2 techs for it, especially if it doesn't feel the tech is as valuable. Some things are damn near impossible to trade for, like distant remote cities on a lone island. Resources can be scarce so resource trading is a pain if you don't have your own resource to trade back.
2) War: The AI has the "appearance" of being out to screw you in war. In an ideal world, everyone gets along until the superior human stomps everyone. In Civ3, the game was designed to be be pretty evil about that, because in the real world other civs sometimes just want to screw you. You have to build up enough troops and defenses to not get screwed. That's the point of the game. If you go without building any troops, the "human" response would be "oh look at those fre cities." C'mon, you wouldn't do the same thing to the AI if it had 20 well placed and well developed cities and about 6 spearmen to your 50 tanks? Frankly, I like an aggressive civ only because that means that when a civ is aggressive, I like to play the "moral vindicator!" or "Righteous defender!" Some people are over dramatic about civ but hey it's what we do
3) Mood: The AI starts out with a simple neutral feeling towards you which essentially erodes over time if you don't negotiate with that AI Civ frequently. Well, as most people will say, they only want to negotiate with another AI civ when it suits them. Great, now think about you being treated that way by another human. Would you not feel bad? Of course you would! My personal complaint here (my main complaint with the AI) is that you cannot repair hurt feelings. The AI is designed to have a "ceiling" where if you've completely POed a civ, you can't get back to "polite" or "gracious" ever. You can get some brownie points, but they will stay furious forever unless you spent most of the game giving them gold, swapping maps, and in general keeping up trade.
4) Workers: the automated AI for workers is both for you and them. I needs to be customizable for the player and it needs better handling of priorities or at least customize them. If it plans on building a road on an unimproved square, and then pollution pops up next turn, it should probably build the road first and not waste the moves it took to get to the point to build the road. Right now, it moves back to a road square, taking one turn, and then goes to clean up the pollution. It's more efficient to let another worker doo the job, but the AI doesn't know how to spatially prioritize jobs for each worker and just reassigns one worker to one job at a time. I would also like an option to completely prevent my workers from crossing another civs territory to another of my cities unless I have a ROP agreement. I don't mind, however, how it works for the AI and I don't even mind the RRs everywhere phenomenon, it makes it easier to defend yourself when everything has RRs.
I think to get a successful Civ AI you have to discuss the details. Trading wouldn't be so bad if resources and advancements weren't so "scarce." Mood wouldn't be so bad if having MPPs didn't force you into war or force you to drop trading agreements rather than giving you options. Works need tweaks.
All in all, the AI in civ is good. It can be better, but it's the details that need to be better. The AI is there to make it harder for you to beat the game. While it might seem like the AI is out to screw you, it's the details that determine whether or not you feel like you were screwed, or you were given a strong challenge.