Is it valuable to look at this from the other side? As a thought tool, I tried to ignore the current list of civics and discuss what civics would make the game better. What are the play styles that civics should be encouraging?
Cool things I can do now with civics:
Choose between a large empire and a compact one.
Save myself if I overextend my empire.
Build a farm-centric strategy.
Prep for war.
Gain rewards for my towns having my religion.
Gain specific rewards for certain religions or civs.
Cool things Id like to be able to do with civics:
Save myself when I have a happiness crisis (other than war weariness). There are a few late-game options that can do this (Republic), but I often have happiness problems relatively early, and I wish there was more I could do in that case. Having an early civic that reduced unhappy faces (without adding happy ones) would be great.
Differentiate my military strategy (magic/melee/disciple/archery/horses). I like the above idea about giving +XP to specific types of units.
Focus on magic. Scholarship is good, but I want more ways to emphasize my magical expertise.
Focus on not magic. Itd be interesting to have one or more civic whose penalty is denying magic. Maybe tie it in with some of the religiously fanatically civics? Reduce the rate at which magic units gain XP? Forbid any spell casting? Turn off certain types of mana?
More options on how to rush production. Currently, its either octopus or gold. I like the concept of limiting whipping to an evil religion, but I wish there was more variety within the Labor civics. Is it possible to allow other ways to hurry production? Spend culture? Spend happiness? Spend research?
More special terrain upgrade strategies beyond the farm path. The farm path (Aristocracy / Agriculture) is great in that it carves out a unique playstyle. Ive heard rumors there used to be a cottage-based civic strategy that got overpowered. I think its worth bringing that idea back, or building a similar mine-based strategy. More ways to encourage radically different playstyles.
Gain an early boost to research. Scholarship is good, but its a late game civic. Id like to have something I can choose to turbo boost my research at the cost of other things.
Specific issues:
(skipping civics where I have no problems)
Theocracy: The conflicting happiness bonus and penalty often make me avoid this, since I often build big empires that tend to have a few extra religions. I don't want to bother computing how much it would help versus hinder, so I don't bother. Would there be a way to minimize the religious competition penalty? Maybe switching it to a culture penalty instead of directly counteracting the bonus Im aiming for?
Theocracy: The XP bonus seems like a big part of this one, but it doesnt seem particularly flavorful. Why would Theocracy make my military units smarter? Would it be possible to reduce maintenance in cities that have your religion? Or just do a blanket reduction in costs for military production?
Republic: I agree with others who find penalizing other players annoying. I don't see an easy way around that without gutting the civic, so I suppose I agree with the above call to just remove it and replace it with something else. Another late-game happiness boost, but maybe with a magic feel or tied to a specific terrain upgrade strategy?
Pacifism: I like the concept of having a civic that rewards you for avoiding war at all costs. But I find GPP too specific of a reward. Especially early in the game when Pacifism could be an interesting option, I dont usually have lots of GPP to make this matter. This could be a place to add an early science boost, or maybe to remove unhappy faces.
Pacifism: The gold cost of this one always scare me away. I dont even know how penalizing it really is in all games, but Ive seen it be bad some times, and most times Im too lazy to bother digging into the numbers to see exactly how bad it would be, so I just assume its bad and avoid it. Remove this, or change it to a different penalty.
Social Order: Slightly better version of Nationhood. Civics that require a certain religion or civ have more pressure to be interesting, and this one doesnt make that cut. Give it more a feel for the religion. I dont play the Order much, so Im not the right person to say what that feel should be. Free promotions (in cities with The Order) are always fun.
Consumption: The Medium upkeep seems at odds with the goal of getting lots of money. Id reduce or remove the happiness gains (which are off of the main goal of this civic as I see it) and reduce the upkeep. Maybe even go further and add a bigger penalty (to health?) or but make the money gains equivalently bigger.
Liberty: This one seems a little torn between the specialist playstyle and the culture playstyle, but it seems to manage to balance between the two relatively well, so I suppose it works.
Arete: Boring. Not enough focus. Compare to the interestingness of Guardian of Nature. I suggest turning this one into a mines-focused strategy. Remove the other bonuses. Add a food to mines, which would really make them useful, maybe too useful. Or something of equivalently radical nature. Increase the chance of finding resources when you dig a mine to something crazy? (although that steps on Earth Manas toes)
Guilds and Caste System: These seem to overlap a bit. The concept of having multiple avenues with which to exploit specialists doesnt bother me, but there are many other interesting strategies that get no civic at all, and these already combine with civics in other trees. Maybe remove one of these entirely and replace it with a magic boosting civic? Or something that focuses on certain military strategies? Or a terrain-focused civic?
Mercantilism and Foreign Trade: I often avoid both just because I either dont bother or cant focus my economy on internal or external trade. Building trade enhancing buildings takes time, and I have no guarantee at the start of that that the costs will balance out. Which means I often dont have any Economy civic choices and am stuck with Agriculture by default. Is there a way to balance out the gold benefits of these civics so theyre less likely to be harshly penalizing? Id be more willing to experiment with trade-light or trade-heavy strategies if I had some confidence that Id end up with a net gain. But Im not entirely sure how to guarantee that.
Compassion: I like the moral spectrum here, and how it plays out in foreign relations. Good stuff. I just wish the later versions were more interesting. Adding a High or even a Medium upkeep civic is often crippling, so I often dont bother with Protect the Meek or Public Healers. Adding more of a custom benefit to these two might make them more interesting. Could Public Healers start some military units out with the Medic promotion? Could Protect the Meek increase the cultural defensive bonus of cities (more civilians manning the gates)? Or give a slight boost to science (Stephen Hawkings is free to think with others caring for him)?
Military Discipline: The XP bonus from Apprenticeship is often more useful than the bonuses this gives, especially when the upkeep is considered. Maybe make Apprenticeship only give XP to certain units, and make this one give XP to all? Or have this one give a free promotion to all/most military units? Free Combat I if you have a Training Yard?
Religious Discipline: I kinda like the science bonus here flavor-wise, but gameplay-wise it seems to step on Scholarships toes. Maybe consider switching the science bonus out to another one of the religious civics (Theocracy? Religion? Arete?), which also allows synergy with Scholarship if you can maintain a religion.
Oh, and I agree with the people who have poked holes in the naming choices. And the ideas for more restrictions on which civs/religions can choose which civics.
bonus from training yard, it might be nice if the other T2 unit buildings had a bonus somewhere, like foreign trade getting a 
with mage guild
to buildings through civics...)
