[U][B][SIZE="3"]Vassalage[/SIZE][/B][/U]

Required Tech: Feudalism
Effect: New units receive +2 Experience Points
Use: For 2 promos (3 with agg) on not-mounted units in Ancient and Classical Teamers. For tripple promoted mounted units in Medieval, Renaissance and Industrial Era Teamers. For tripple promoted German Tanks in Modern Era Teamers. For additional Promo in Ironman/ffa.

As you can see Vassalage can be used in almost every setup. However it is only used by the whole team in Ancient and Classical, because later on you have to choose between Bureaucracy and Vassalage on the Legal branch, while you have Theocracy available. So for getting 5EP on your units, you will rather use Theocracy. In Ironman/ffa this is different, because you do not necessarily have a religion to use Theocracy. In this case you will need to use Vassalage for the additional promotion.
In Medieval Teamers you could theoretically use Vassalage for another promo on melee units, but for economy and tech path reasons this isn´t used in any of the currently common strategies.
In the midgame eras you can build tripple promoted mounted units, if you either are Charismatic or Mongols and use both Vassalage and Theocracy. Since in those eras there is a focus on mounted units (Knights, Curassiers, Cavalry) and the third promotion provides you with formation (+25% against mounted units) this gives your units a significant advantage. The same can be done for all units with Pentagon and Chm as soon as it becomes available.

[U][SIZE="3"][B]Bureaucracy[/B][/SIZE][/U]

Required Tech: Civil Service
Effect: +50% hammer, +50% :4wirt: in capital.
Use: Increasing science and production output in OCC, Ironman/ffa, and all Teamers as soon as it becomes available

Bureaucracy will be your standard civic from as soon as it becomes available, except if you use Vassalage for aforementioned reasons or have to draft with Nationhood later on. The reason why it is so strong, is that the fifty percent bonus multiplies commerce and not science/money. This is applied before other science/money bonuses are applied to their share of the commerce. If you push your cap with Academy and University of Oxford this leads to huge effects.
Bureaucracy is especially useful on Teamers, where you have very few cities, so the effect in relation to your whole empire is bigger.

[U][B][SIZE="3"]Nationhood[/SIZE][/B][/U]

Required Tech: Nationalism
Effect: +2 happiness from barracks, +25% Espionage, can draft X units per turn (dependent to mapsize (3 on small and standard))
Use: Drafting Rifleman when they are available (ffa/Ironman, Renaissance and Industrial Teamers, for espionage economy in Ironman/ffa.

Drafting units with Nationhood is the by far cheapest way to get units, while Rifles are up to date. Earlier the units are too cheap to justify not going Bureaucracy and later on it costs more then one population, making it not that effective anymore. Though the time frame for its use is pretty limited, it has huge impact on the game.
The biggest point is, that it makes wars against players who can draft rifles virtually impossible, before you can not at least build infantry in Ironman/ffa. The defending player wont care for the unhappiness from drafting, as soon as he realizes he is losing. So he gets massive amounts of cheap units, while the attacker cant draft that much, because of unhappiness problems.
In Renaissance Teamers Nationhood makes teching for Rifles even more interesting, because you not only get better units, but can also build them very cheap. The same happens on Industrial era with Riflemen being available from the start. In both eras so called draft-phases are used: Since players will be spiritual in most cases, they switch to Nationhood for 5 turns and draft heavily, then switch back.

[U][B][SIZE="3"]Free Speech[/SIZE][/B][/U]

Required Tech: Liberalism
Effect: +2 :4wirt: from town, +100% :4kult: in all cities
Use: For Cottage Economies and Cultural Victory in Ironman/ffa

This one is very powerful and very simple. If you play a cottage economy in Ironman/ffa and have reached a certain amount of towns (about 20) you switch to Free Speech. The effect speaks for itself: about +30% raw commerce is a lot.
If you head for a cultural victory adopting Free Speech as soon as possible is a must of course.

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