It seems you are discussing about something you all agree.
Complete city specialization is as dumb as a complete mess about what to do in each city. None of you defend any of these views, but all of you think the person with the "opposing view" defends one of these options.
It started out with Stables being a build-in-every-city-building. While I agree with Vokarya that Stables could give +1

(it makes sense and

is indeed overwhelming at least until the Renaissance), also I disagree it
is a build-in-every-city-building. Being a XP-only building it's easy to forget to build them in economic cities.
Of course you may say if you play a game where having 10 cities is being big, then the analysis won't be true enough. With 10 cities you may easily feel a Stable is a build-in-every-city-building. But when having 30 cities puts you on the average size of the bunch (around 5) of top civs in the Renaissance, a Stable will definetly not be a build-in-every-city-building. You'll have cities that are just for economic purposes, so no barracks or walls or stables or ballista turrets. If you want to compensate that full-of-bonuses AI, you'll have to put all non-economical buildings to the bottom of the queue for some cities.
As I disagree that stable is a build-in-every-city-building, I also disagree giving it

makes it less wanted for every city.

is one of your least problems in CIV. While

people don't work, for each

above the limit, you just lose 1

.
Many times it's better to let cities become
because the penalties are far lesser then the bonuses of working more tiles and having more population. Of course there may be options or mechanics that take

into account, but I never experienced something really terrible to make me think twice.
Then Joseph attacked the concept of city specialization. I agree that a game only focused on city especialization would be horrible, but a game without any specialization would be also awful. Anyways, I didn't agree with Vokarya's concept, so I can't comment on Joseph's denial of the Stable
Afforess gave a brief answer, so it's hard to comment on it.
Arakhor and Rezca gave explanations about what they make with city specialization. These may make sense in smaller games, but in bigger games they don't make that much sense. Of course there are NWs that force you to choose the best cities for them, so actually you specialize some cities. But in bigger games you'll always have more then 1 city to majorly specialize in a sort of function, and many times the Oxford University city will make not much more

then 2 other cities that also focus on

.
Which brings me to the point I wanted to make: City specialization isn't as powerful or varied as many here think, but is a must to a better game nonetheless. It's all a matter of using the numbers in your favor, so for that to be well explained, firstly I'll start with the most important modifiers for city specialization:
National Wonders.
National Wonders are the truly specialization factors for you. They have a limit per city, and they rarely give similar bonuses. World Wonders don't fall into this category because many times you must think twice in building a world wonder on the best city for it, or in the city that builds it faster (because you may lose it to someone else). So put in practical terms, National Wonders are best used in cities specialized for them (Oxford needs to be built in a

city, while the Wall Street is nice in your

Holy Shrine), which forces you to make suited cities for these NWs to get the best output.
The other important factor of specialization is
Military. Here we have 2 distinguished specializations (which may be mixed too): Elite Troops or Fast Recruitment. One is specialized in XP (which goes well with settled GGens), and the other in

for troops (e.g. Heroic Epic city). It's nice to have a single elite troop-producing city, while fast-producing ones are more common and easier to make (but that Heroic Epic shouldn't be wasted on a bad city anyways).
Besides that the only other thing you may want to truly specialize is GPP for wonders, GAs, Corps or other effects.
And why do I say that? Because your best

city may also be your best

city and

city just by changing the sliders. Also

may be converted into science, gold or culture, and are nice to combine with military cities. Military cities should be able to contribute nicely when you don't need to make more troops, instead of only being good making them. Also your diplomacy will matter much more to what to do in your cities then what exactly they are specialized for:
A

city is a good candidate for GPP, but also a good city for drafting;
A

city may build the army, or may build science, gold or culture;
A

city will give you what the slider dictates;
So technically Joseph has a better way of handling city specialization then you who defended it:
The best specialization is the one you do at the moment. Of course you must not try to make troops on a city with no production, or make the Oxford on your Holy Shrine, but having cities with several different kinds of buildings gives you more versatility to change what to do suddenly. I may don't have a

city, but if I have plentiful of espionage buildings in several cities, putting my slider in 100%

for one turn may compensate more then focusing on having at least one city dedicated to espionage (spy specialists and buildings). The same may happen with gold and science: if you change the slider, the cities will contribute a lot differently. Also changing some cities to build gold or science is another way of focusing on these things when the moment is right with cities that could be your fastest unit-producing cities just before.
And an expert on civ will say that your needs may change as slow as several turns, or as fast as within the same turn. Having versatility is the key. But it has a price: The more versatility of cities the more vulnerable in both Technologies and Army Size you'll be (because versatility demands buildings, which are

not spent on

or Troops).
That's why this game is so awesome, because actually all approaches listed in this topic may be good or bad depending on the situation. The best outcome you may take from all of this is that you must learn how to discover exactly what's the best to do at each moment of the game, and the worst strategy is the pre-made, preferred, monotonous one that doesn't care about the changes, just believes in static values (E.g. I always build the Oracle because I like it, or I never put GGens in troops). This may win Noble games. This won't let you survive long in harder games, unless you're lucky enough to have chosen the best strategy for the conditions the game imposed on you.
A wise player once said "If there was only one right way to play the game, you would not be looking at a strategy game. You would be looking at a puzzle - to be solved once and be done with it"
This explains a lot! Thanks Rezca