Required Tech:
Bronze Working
Effect: Can sacrifice population to finish production in a city
Use: Main means of production till Modern age

Slavery is the most efficient way to produce till you either have a fully developed cottage economy running Universal Suffrage or workshops with State Property and Caste System. That is because with granaries growing your city and slaving that pop gives more hammers, then working mines with that pop during the same time.
Till then running Slavery on the Labor civic branch is the standard, everything else the exception that needs a good reason.
Efficient usage of Slavery is one of the major aspects of micromanagement in civ multiplayer. Due to its complexity I can not fully elaborate on it here, but I will try to name a few basics.
Direct slaving (without producing beforehand) is inefficient (50% higher cost).
You have to prevent unhappiness from stacking up too much, so try to slave as much pop as possible when slaving.
Try to generate overflow by slaving shortly before you would have to sacrifice one pop less in order to do so and finish another project with that overflow. A city that is designed for slaving units should grow each turn. Small cities grow faster, bigger cities can work cottages/extra hammers. Which size you need depends on the food available.

Required Tech:
Effect: Workers build improvements 50% faster
Use: Speeding up buildup with spiritual leader in Reni, Indu, Modern, Future start games

If you are Spiritual on a Renaissance or later era start game, you can go Serfdom for a few turns early to speed up your buildup before you start running Slavery. The usual way to go is to adopt Slavery on the first turn, slave your initial pop into workers, then switch to Serfdom as soon as you can for about 5-8 turns and then go back into Slavery.
Otherwise Serfdom is actually one of the most useless civics.
[B][SIZE="3"]Caste System[/SIZE][/B][/U]

Required Tech:
Code of Law
Effect: Unlimited Artist , Scientist, Merchant Specialists; +1:4prod: from Workshops
Use: Making GP in Ironman/ffa, Cton, Medieval to Future era teamers; Increasing production of Workshops in Industrial, Modern, Future teamers.

You are only running Caste System longterm when using massive Workshops for producing units in Industrial/Modern/Future teamers. Doing so, you adopt Caste System together with State Sroperty as soon as your cities have enough Workshops available. In Industrial teamers you have to research State Property first and do it then, on Modern and Muture you use Serfdom for the first 5 turns and then change your civics.
The other common use for Caste System are so called GP phases, that usually also include Pacifism and often a Golden Age.
If you are non-Spiritual in Ironman/ffa/cton you can use a golden age, then switch to Caste System and if available Pacifism on the first turn. Then you put in massive specialists, even starving your cities. During Golden Age those make another +100% GP points. This way you generate a few GP, then switch back on the last turn of the Golden Age to avoid Anarchy. This is commonly used for generating Great Artists in cton and often a side-effect of midgame GAs in Ironman/ffa.
If you are Spiritual you don't need the golden age to avoid anarchy of course, so you can do it anytime. This is often done by people playing Gandhi in Medi/Reni/Indu teamers to get Great People for bulbing techs.

Required Tech:
Effect: +100% growth for cottage, hamlet, village; :angry: penalty for civs without emancipation
Use: Speeding up growth of cottages in Ironman/ffa and Indu teamers.

The only real use of Emancipation is to finish growing your cottages in Ironman/ffa with a cottage economy when finishing to grow your cities to max. population after having teched Democracy.
Still because of the unhappiness penalty for other players often everyone ends up running Emancipation in the end, because as soon as someone adopted Emancipation a chain reaction is the result.
Using Emancipation in Industrial Teamers is a little out of date, because workshop economies are more common today, but might still be used on a single player running cottages to tech for the team.

[B][U]See also:[/U][/B]
[URL="http://apolyton.net/entry.php/17-Civics-in-Focus-I-Government-%28Civ4%29"]Part I: Government[/URL]
[URL="http://apolyton.net/entry.php/18-Civics-in-Focus-Part-II-Legal-%28Civ4%29"]Part II: Legal[/URL]