As probably most Civ 4 players, I'd like to win a game of each victory type at least once. Having won a space race victory already in my first game, I now wanted to go for a cultural victory. Cultural victory means that you need to get three cities to legendary status, meaning 50000 culture in each of the three for a normal game! That is very hard to do, indeed it's one of the hardest victory types in the game, maybe apart from a diplomatic victory. Why? Because it needs a lot of strategy and planning ahead, moreso than any other victory type. You can turn almost any game into a military or spaceship victory, but you cannot decide mid-game that you suddenly want to go for a cultural victory - that won't work!
But I wanted more. Expanding to a large empire, then turtling in to cruise my three culture cities to legendary status sounded too similar to a spaceship victory game, and probably too easy. I also wanted to get more experience with trading and diplomatic relations, and I knew I would reach a tech lead in a normal game which means I wouldn't have to interact much with the other civs.
So I decided to play this game as a 3CC (a three city challenge): I would not be allowed to have more than three cities at any time! This had multiple consequences: On Monarch, I expected it to be hard to keep up with research, which means I would have to trade a lot. I would most probably also lack critical resources, which means even more trading to do. And last but not least, with all my cities concentrating on building culture, my military would be comparatively weak, and fighting a war with only three cities against much larger empires would be very hard to do. So it would be in my best interest to keep good relations to the other civs to avoid war entirely!
As mentioned above, a cultural victory needs a lot of planning and strategizing ahead. What now follows are my preliminary thoughts on how to achieve this, which might serve as a starting point for others to play cultural victory games themselves (although it's by no means the only way to do this!). If you don't want to read this but jump right into the action instead, you may of course skip this.
The first question is, what civilization should I choose? What traits will be helpful in achieving a cultural victory? While I'm sure it's possible to do it with every leader, some traits are stronger than others in regard to this kind of game.
Most probably the least useful of the traits. You want to avoid wars at all cost which would slow down our cultural development, so the experience bonus won't help us much. The production bonus for barracks and drydocks is useless as well, as they don't give culture.
Not very useful either. While the extra health doesn't hurt, the bonus is not directly tied to culture and would be equally good for any victory type. In my 3CC game it's even less useful.
This trait reduces the upkeep cost of civics, but the civics we want to adopt during the game won't be expensive anyway - especially Free Speech and Pacifism have no and low upkeep, respectively. When you want to improve economy, I'd say go with financial instead.
Improves your finances, which won't help you with culture directly. However, if this will help you keeping up 100% research longer, which in turn might lead you to get key techs for cultural buildings or wonders sooner, then this is a good thing. There are better traits for cultural victories in my opinion, but choosing financial won't be a mistake either. In my 3CC game on the other hand, this is not so good, as it won't provide me with much absolute extra income.
This one is juicy, as the production bonus on wonders will help you getting key cultural wonders in the first place (which otherwise might not be so easy, see my game report later on *cough*). If you're playing on higher levels, or if you lack stone and/or marble, this trait might come in very handy. Still, as with the financial trait, while I think choosing this trait won't be a mistake, there are better traits.
This one is tricky. On first glance, this looks like *the* trait to choose for a cultural victory, but this warrants some more thoughts. Your three going-to-be-legendary cities will receive an extra +2 culture per turn - which in the end won't amount to much! For your capital (most likely one of your legendary cities), this amounts to about 800-900 culture overall depending on how long the game will last, plus some bonus from buildings which give you +x% culture per turn. So this trait will give you something between 1000 and 2000 culture for you capital, and even less for the other two cities (because you found them later)! For a normal game, that's only about 2%-4% of the 50000 culture you need, and compare that to the effect of one great artist, which will give you 4000 culture...
For normal games, I like this trait because you get a free border expansion in new cities to gain access to tiles and resources outside your initial city border. However, since you will be building culture in your three main cities rather sooner than later anyway, that won't matter much here.
The bottom line: Creative sure is better than Aggressive, Expansive or Organized, but not the no-brainer trait it looks to be on first glance.
This trait's primary effect, no anarchy, won't be extremely helpful but it's still nice. You will change civics several time during the game, and every anarchy will cost you culture. Depending on how the game will progress, you might even be forced to change civics more often, like when you're attacked and want to switch from free speech and pacifism to more helpful, military traits, then back again after the war. Especially later in the game, one turn of anarchy can cost you hundreds of culture per city. Overall, I think it will provide you with less culture than being Creative, though.
But there's also the secondary advantage: Double production speed on temples. This will most probably kick in more than once per city, as you will build more than one temple in each of the main cities. And last but not least, spiritual leaders are the best to found early religions with thanks to their starting techs, which plays nicely into the cultural theme.
So, all advantages combined make this trait at least as good as Creative, maybe even better if you're forced to change civics often throughout the game.
I've spared the best trait for last - this is the killer trait for cultural victories! The +100% birth rate for great people is huge. You won't be able to get three cities to legendary status on their own, so you will need great artists to help you out, and (depending on level) you will need a lot of them. +100% birth rate means you will get approx. two times the number! And the trait's production bonus on the university won't harm either, so I'd say winning without this trait would be a lot more difficult.
So philosophical/spiritual, philosophical/creative, philosophical/industrious and philosophical/financial would be the
best combination of traits for a cultural victory, which suggests taking Saladin of Arabia, Frederick of Germany, or
Elizabeth of England (there's no phi/ind leader!), but other leaders are possible too. For a challenge, try Genghis Khan
of Mongolia (agg/exp)...
Now how do you get your three cities to legendary culture? There are two ways: Cultural buildings, and great people.
There's a simple rule for maximizing culture in your cities: Build every cultural building you can, and build them as early as you can. The earlier a building is finished, the more time it will have to generate culture, giving you more absolute culture in the end. There are two types of cultural buildings: Those who generate a fixed amount of culture every turn, and those giving you a boost of +x% culture per turn. The former include (but are not limited to) temples, libraries, universities etc., which give a modest amount of fixed culture, and wonders, which take longer to build but which will reward you with much higher amounts of culture (usually, +8 or +10). The latter are the cathedrals of different religions, broadcast towers, some wonders (both world and national) like Hermitage, Rock'n Roll, and others.
While buildings which produce a fixed amount of culture are a no-brainer and should be built in every of your three main cities, the other buildings require a bit more thought. Because they boost culture output that's already existing, the best city to build them in is the city that generates the highest amount of culture per turn, which in most of the cases will be your capital. That is because that way, the absolute amount of culture you receive in the end is maximized. Say, for example, your best two cities are generating +100 and +50 culture per turn. Building a cathedral (+50%) in the first city thus will give you an extra 50 culture per turn, while building it in the second city will only give you 25 culture per turn! The only exception to this rule is when you're certain that the first city will reach legendary status before the end of game on its own, because after that, all extra culture would be wasted.
Face it: You won't be able to get three cities to legendary status by buildings alone, especially on higher levels where you might fail to get some of the wonders. So you will have to enlist the help of great people, great artists in particular.
A great artist can either discover a technology, can be turned into a specialist (+12 culture per turn, +1 gold), or can create a
great work (+4000 culture once, for normal games). Using an artist to discover a technology is obviously a waste, but
the decision to turn him
into a specialist or creating a great work with him is a bit trickier. When will the specialist have generated more
culture than a great work? The calculator says at a rate of +12 culture per turn, he will have generated more than 4000
culture after 333 turns. 333 turns is a very long time - but also not correct in many cases.
You also have to consider buildings, civics and other effects that boost cultural
output of your cities, which enhance the specialist as well while not improving the culture you get from
constructing a great work. But considering that you'll likely get your great artists
rather late in the game and that you'll get culture booster buildings even later, I find creating a great work superior
in most cases. You should consult F8 to see how many
game turns are left, and subtract a good amount of turns
(80 - 100, depending on difficulty level) assuming that someone will have built the spaceship way before 2050AD. Then you
should be able to better estimate
whether creating a super specialist or a great work will bring you more overall culture.
The question remains where to create the great work in. If you can afford it, keep the great artists and delay that decision until you see you could win by creating great works with all of them, because during the game it can be hard to judge sometimes which city will trail behind in culture later. But most of the time it's no mistake to create the great work in the city with the least amount of absolute culture if that city isn't generating a lot more culture than the the other two.
Depending on how many wonders you will be able to build, you will need a lot of great artists to win the game before anyone builds the spaceship. So how do you do this, considering that every great person will be more expensive to generate than the one before?
Again, there are two ways to generate Great People points (GPPs): Wonders and specialists. There's a catch though: Wonders and specialists produce GPPs for a certain type of great person, for example the Colossus produces GPPs for great merchants, or scientist specialists generate GPPs for Great Scientists. So if you have a mix of different sources for GPPs in a city, you are not guaranteed to get the great artists you want!
So the idea is to specialize one city, most probably your capital, to produce great artist GPPs only. The only buildings
you want to build there that have something to do with great people are buildings which generate GPPs for great artists,
and buildings that enhance the birth rate of great people. Also, the only specialists you want to hire there are
artists - no scientists, no engineers. If possible, try not to dilute the GPPs with non-great-artist points!
If you have a 98% chance of generating a great artist and 2% of generating a great scientist, you might get unlucky
and produce the scientist - and have just lost 4000 culture! 
So try to build
all the other wonders like the Great Library, the Colossus, the Hanging Gardens etc. in your other two cities.
Every great person produced will increase the cost for generating the next great person. Because of this, you will need
to generate A LOT of GPPs later on if you want to have your 10+ great artists at the end of the game. Every time your
GPP-specialized city is unable to produce a cultural building (that means, has nothing really useful to do to drive us
forward on our path to victory), don't be tempted to produce other things like military in it. Instead, have your
workers create a huge surplus of food in that city, emphasize food there, and add as many artist specialists to the city
as possible, until the city is not growing anymore. For this, the Caste System civic is best, as it allows you unlimited
artists. Each artist will not only produce culture, but also GPPs which will be further enhanced by buildings like
the Parthenon or your philosophical trait. That way, you can generate about +150GPPs per turn, and you will soon drown
in great artists. 
One other trap to avoid is the temptation to produce other types of great people in other cities. While having one or two great scientists to construct academies in your three main cities is nice, or a great prophet for religious shrines, be careful not to generate too many of them. Why? Because every great person will increase the cost for the next one, so producing that great engineer to help you rush a wonder will delay your next great artist even longer! Try to find a balance there.
While researching, you should prioritize techs which will give you culture buildings, wonders, religions, or civics that will help you. Religions especially can be nice, as you can spread them into your main three cities on your own, which will enable you to build temples there and the important culture-boosting cathedrals later.
Obviously, it is very beneficial to be the first to discover Music, as this will grant you a free great artist. It should
also be a top priority to get Liberalism for the Free Speech civic (+100% culture in all cities) as soon as possible,
and Philosophy for the Pacifism civic (increases birth rate of great people by 100%). As mentioned before, Caste System for the
unlimited specialists is great too, but once your city is large enough to support 10+ artists, you will have the
required tech anyway. And if your economy can afford it, adopt Mercantilism (comes with Banking) for a free extra artist
in your city (which hopefully will be joined by a second free artist from the Statue of Liberty
).
So after all this long-winded, theoretical strategizing, let's see how this plays out in practice!
