Depends on the theme of the campaign and what the players want out of it really.
What types of Governments do I use? Generally it is you name it, we have it. Though, again, that depends on the situation. Is this a campaign that will involve several nations or an established empire?
I have had the God-Kings, Magocracies, Aristocracies, Republics, Monarchies, Matriarchies, Stratocracies, and more.
My current homebrew is that of a Roman empire near the height of its power. An Emperor as well as a council of officials (not elected) rule the provinces. There are obvious power struggles that happen, and several hooks to get the players involved. Some of the group are pretty 'meh' about it. Liking only the perks that come from helping a political figure on the rise, while one has throw her hat into the ring and is working to gain a membership on the council.
That means, my campaign has to fluctuate how much politics and intrigue happen, sometimes from session to session. Also sometimes when I might be drained from a long week, and can't wrap my brain around game of thrones ways of thinking.
I guess it depends on how in depth you want to go with it. This time around, I wanted to really, really work on my world building. Right now, it is paying off. That extra attention to detail has come in handy due to the Baroness' interest in the government. It could have easily gone the other way though, and I could have had this massive government structure detailed like the Imperium of Man in 40K (mine isn't

) and have no player actual peek behind the curtain or show interest.