Not sure if this is completely germain to this discussion, but the way I wage war in Civ4 is to plan, plan, plan, and bring overwhelming force. I start a war with the intention of completely wiping out the enemy civ; rarely will i sue for peace, and only if my plans have gone horribly wrong or I've made a mistake. And even then, a peace treaty is only a tool that enables me to regroup for 10 turns and go at them again.
My games generally follow this pattern: Build 4, sometimes 5 cities and prepare for the Barbarian invasion. Fight off the barbs while building up my nation. I have a flowchart that I follow for tech research, which roughly gets me bronze working/alphabet/civil service as quickly as possible. Once I get Civil Service, (and can sustain a large number of cities), I move towards my first war - by this time I've identified the other civs that I will take out, and in what order. This depends on the map & etc of course, but I'm usually being squeezed, cut off, or need to expand into another civs' territory. Of course If I have room to expand into un-occupied land I will do that first, and pause after building a every few cities so that my economy can recover. But at some point in every game I find that I need to take out other civs in order to stay competitive.
I'll target the weakest civ that I have a common border with first. I'll take out other civs from the weakest to the strongest. My thinking is: I myself am weaker earlier in the game, my combat units don't have a great deal of experience yet, and will gain that through fighting. And by the time I fight the strongest civ, I will be at my strongest.
I'll build several armies and assign each of them 2 to 3 enemy cities as targets. My armies I make up of 4-5 siege units, 15-20 melee/gunpowder units, and assign 1 or 2 stacks of 4-5 cavalry to each. The cavalry does not stack with the army; they perform the traditional cavalry functions of screening, reconaissance, blocking, etc for my armies. Civ4 portrays cavalry very well and they are indispensible. I plan my invasion so that the armies converge towards the final 1 or 2 cities, so that I can merge them - because by the time they have taken several cities they will be weakened, and usually the enemy makes a 'last stand' with all their remaining units in the last remaining city. Usually the enemy will sally forth with an army to attack my units, or go for a border city. i harrass them with cavalry, and am always glad to receive their attack, because they just whittle themselves down and can then be wiped out or ignored at my leisure.
I choose the shortest path to each target and do not stop to pillage, or to attack enemy units that are outside their cities. Never lose your focus and chase targets of opportunity, you'll drag yourself to a halt. I do not pillage - for a couple of reasons - it slows down the invasion which is a game-killer. I do not want a long war, I want to quickly take each city in turn and end the war as soon as possible. Pillaging for a little gold is a waste of precious time. I never fight a war unless I plan on taking out the whole civ. So, if I pillage, i am really just destroying improvements that will be mine in a few turns. In other words, I'm pillaging my own improvements!
I move my army next to a city, with cavalry on the flanks, and far enough away from the city so that the enemy won't send out tropps to attack them. The cavalry gives me eyes and protects the army from attacks to the flanks. I hit the enemy city with a barrage of all the siege units, and then attack. rarely will I bombard a city twice, the trade-off in lost time is generally not worth the advantage of reducing defenses. I'll bombard, then attack on the same turn, take my medicine, and take the city. I'll only raze a city if it's very poorly placed. If I find I've run up against a heavily-defended city, I may set in and bombard it while I move another army over to help. very rarely will i use my cavalry to help take a city - I need them for other roles, and they are too precious.
After I've taken another civ out, I'll regroup, build my armies back up, allow my financial situation to catch up, and hit the next one. the thing I hate the most is when a civ has built a city I can't reach, heh. But it's a small matter, after I've destroyed their main civilization they are eliminated as an effective competitor.
Anyway, the point of all this is to show one way of waging war - and what if the AI fought wars in this way? You'd have your hands full I think, trying to stop such a 'blitzkrieg' attack by multiple large armies. I've not played a game where I didn't wonder, "What the heck is the AI thinking?", because it doesn't react intelligently and is too predictable. I'd like to see several AI types, some that are smart warmongers, some that are so-so, some that try to win via diplomacy, culture, science, etc. and have new civs be assigned an AI randomly at the start of the game. Furthermore, allow the leaders for a nation to be changed, and bring with them a possible AI-type change. Now wouldn't it be cool if your peaceful neighbor suffered a coup and the new leader was a violent warmonger?
I think the AI is where the most improvement could be made, and it's a shame it's not the target of more modders. So much could be done with it that would keep Civ 4 fun and exciting for years to come.