I'll add to what The Capo said;
Anarchism - well of course The_J suggested it. Look at his avatar.
Only things I can think of is 0 civic maintenance, no state religion, maybe 0 city maintenance, but severe production, research, and commerce penalties.
Communism -
As an ideology though, I'd say all melee, gunpowder, archer units get city defense bonus. No specialists allowed, can use hammers for espionage points, +1 hammer per population in all cities. Double Production speed on Projects.
sounds good, maybe make "state property" require communism, or maybe less penalty for drafting or something like that
Democracy -
Can use money to rush projects.
Can not have vassals.
+ I'd say universal suffrage and emancipation could require Democracy, at least universal suffrage for sure. Maybe some risk of great depression like in RFC. Bigger penalty for war weariness in offensive wars, and 0 penalty for devensive/call from ally.
Fascism -
No war weariness or disorder from fighting wars (you declared war on our motherland etc.) Unlimited specialists. Free corporations.
the fundamental belief of fascism being that human beings are motivated by glory and heroism rather than economic motives, in contrast to the worldview of capitalism and socialism
so I'd say no to free corps but I like the rest. Glory and heroism being the key here, so definitely less xp required for GG spawn, perhaps free xp in cities with state religion. that type of stuff.
Dictatorship - maybe higher city maintenance or at least for distance from palace. Or even civic maintenance. Increased military unit production and/or xp. Maybe unhappiness in largest cities, or perhaps even a risk for revolution (or higher) not sure if your using revDCM.
Theocracy - I'd say definitely a penalty to research to show the narrowmindedness. Aside from that the religious buildings should get better bonuses, the church functions should be much more powerful, and followers of the faith should get additional bonuses (like extra xp, or something else more creative)
Monarchy - maybe allow some type of "personal union" or royal marriage with other nations with a monarch, so that they can either join the same team temporarily or temporarily increase relations drastically. Risk for pretenders to the throne (revolutions) again not sure...