I am fast coming to the conclusion that the way you win CivIV is the same way you won Civ I, i.e., by going to war early and often.
All the advances in the game, whether they be monetary advances (gold), science advances (beakers), or cultural advances (little purple flutey thingies)—are additive in nature. The more you have, the faster you advance.
You can either manufacture these things (via improvements, population growth, wonders, and so on)—or you can steal them. Stealing is not only much faster, it hobbles your opponents as you go along.
When you capture a city, not only do you steal the city itself, you steal all the labor that went into it—its improvements, its towns and villages, and its developed resources—plus a boatload of gold.
The money you can use to keep your science pumping—even if you're running sizeable deficits—and the continual infusion of science beakers from conquered territory (often augmented by Academies your opponents have helpfully built for you) can really push your Science into the stratosphere.
The real challenge of Civ IV is to maintain a smooth, unbroken curve of conquest and expansion until you've established such a powerful lead no one will ever stand a chance of catching you. Then you can win as you choose.
Civilization IV ain't SimCity. It ain't a building game. In the higher difficulties, it's all about war, war, war. That, in a nutshell, is the essence of this game.
I'd agree that military knowledge and use is essential in the game, but you don't HAVE to war early and often, and sometimes doing so is suboptimal.
Don't get me wrong, I love warmongering so much that I HATE space and culture wins (I do use diplo wins to end games earlier - aka the "vassals vote for you method). Still, if there's a lot of room to peacefully expand, it makes more sense to do that first and THEN take the lands from the AI. You can often wall off land, keeping nearby AI's smaller than they'd normally be and making conquering them less difficult. You may want to delay for a more hammer-efficient unit to conquer with or so that your opponent "builds a shrine for you" etc. also.
For me though, everything I do is intended to further a military advantage (except for doing something like building the UN, which isn't military but is often the culmination). Even within that constraint, war isn't ALWAYS optimal, you have to pick your time and targets
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Also, I don't like getting the mids, I like playing the map. The exception is if I start with stone and I'm playing LAN with my roommate...he relies on the "pyramids strategy" quite heavily, and it's fun to watch him squirm when they go in 1500 BC to me because I settled my 2nd city on stone and chopped them
. Noble AIs suck anyway so screwing him is my optimal play in those games IMO
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Normally though, for the hammers it takes to make mids I'd rather make military or workers/settlers to claim good land, run HR, and work good tiles while running a few library specialists here and there. I often find this barely weaker techwise than the mids early game, and it quickly overtakes a pure mids specialist strategy as you tech CS/cities grow.
Edit: More relevant to your OP, I also skip TGL unless I am industrious/have marble - again for the investment it requires you can often just out-do it with traditional means.
One wonder that seems to be the bees knees or something lately is the great lighthouse - and using it i've found it's nearly as powerful as the mids. Even then, a lot of maps don't shake out where building it is better than units.
Of course, any of these wonders are equally useful when captured
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