My take on the gov'ts:
Despotism: Great unit support. Pop rush is better at the beginning of the game since you have no money. Horrid corruption and the tile penalty are its demise once cities start to get large. Don't be too quick to leave or you may find yourself running a deficit.
Monarchy: For the serious war monger only. I mean the Always War strategy. OTOH, if you get it from an AI and have a bunch of cities over size 6 and you're religious and you're not ready for Republic, by all means switch.
Republic: Quite simply the best gov't in the game (in c3c). Decent unit support for cities. Paid labor plus the commerce bonus are the ideal combination. Corruption far below Despotism. WW is manageable if you keep wars short.
Feudalism: Pretty much worthless. Maybe, if you're religious and for some reason you have a lot of close packed tiny cities - but why would you want this when the Middle Ages has Banks and Universities and very desirable wonders that are way too expensive to build in small towns? Also, units start to get pricey: 60 for muskets, 70 for knights, 40 for cannon, 80 for cavalry.
Democracy: You need 2 optional techs for this, plus the lost turns in anarchy: That's about 16 turns of wasted/lost research. No thanks. I'll take Magnetism, Steam Power and Military Tradition a the end of the Middle Ages/start of Industrial. No unit support. Horrible WW. Occasionally you can get this from the AI in the Industrial Age once you've traded for all their gold and luxuries. I would only switch to this if I had a continent all to myself and had no plans for war for a long time. If religious, it is a good way to get/keep a tech lead in the Industrial Age and have great productive capacity. I sometimes use it to get to Tanks quickly.
Fascism: Again a gov't for a specific scenario: small/medium empire with large cities/metros AND you plan on conquering the world. Domination is harder with Fascism because of the culture penalty. You're better off razing captured cities. Unfortunately you need 2 optional techs for this, however one of them is Nationalism which you can often trade for.
Communism: Great for large, far flung empires. Allows all cities to be productive. Good for conquest and domination. Again, you need 2 optional techs, but Communism is useful anyway because it allows police stations. To get full advantage of Communism, you want Espionage for SPHQ. Another optional tech but Espionage also allows Intelligence Agency which is useful even if you only use it for the F3 screen.