Monarchy is actually pretty good if you are going heavy Warmonger. Once you get large you want to switch to Communism though
Republic is good for a moderate Warmonger (war is not your primary strategy, but you are planning some conquests/know you might have to risk a long defense 'reprisal war').. You have to be fairly well developed in the happiness department before you shift out of Monarchy (and your army size has to be well managed.)
Democracy is only good if you can maintain peace/Really short wars (good if you are reasonably powerful and going for a peaceful win..not planning on conquering anyone else, and are capable of scaring most empires from trying to conquer you) If you are religious, then you can switch into it during periods of peace and back to a more war oriented government when you end up with wars
Feudalism is good for a lot of small undeveloped cities, a semi-warmonger strategy of Mass units, (good if you are behind, lots of cities with only a few ancient era buildings pumping out nothing but low-tech units.. to help you catch up)
I haven't played with Fascism, but it seems like a slightly altered version of Monarchy for when you are trying to build up for a conquest (better for supporting/building an army, less effective for making use of newly conquered lands..which usually need to be starved out to start before becoming secure and productive)
Communism is what you will want to switch to once you have a massive empire (you are going for a domination or conquest win.. your core cities become less productive, but ALL cities become productive allowing a rapid utilization of conquered lands)