The amount and variety of politics is dependent on the campaign setting and group buy in. Some settings favor politics, some don't. Sometimes we feel like getting political, other times we don't.
For example, in the campaign where we played space demons invading a zombie-infested planet, there was unsurprisingly little politics. There was a bit, such as the time our CO was arrested for shielding us when we disobeyed orders (I forget exactly what, but we were doing what needed to be done), just not much.
On the other hand, the recent Underdark campaign I played in was heavily driven by politics. We chose to back a well-positioned trading town run by a council made up primarily of successful merchants appointed by the medusa who was head of the council. One of the PCs earned himself a seat on the council, whereas my character was sometimes called in as a special advisor (they didn't want to give him a seat because of his ties to the thieves' guild). There were a lot of political machinations going on (some of which we failed to unravel, to our own detriment). The local duergar kingdom had trade agreements with a republic of deep gnomes, but the king coveted our trade town. The gnomes had recently made a giant leap forward in technology (which we later learned was salvaged from a crashed alien spacecraft) and the head of the engineers was poised to take the election from the traditionalist head of the wizard college (who was currently in charge). To dissuade the duergar king from attacking our settlement, we stole the plans for the gnomes' new tech and framed the duergar. Later, when we were more concerned about an army of mind flayers heading our way, we forged an alliance with both groups by returning the plans to the gnomes and convincing them that a shadowy group of goblins (who had been up to all sorts of mischief in that area) had stolen the plans and framed the duergar. This is a vast oversimplification of what happened (a theocratic monarchy of humans from the surface was also involved), but doing it all justice would require a novel.
I would say that at least our trade town's council would constitute an "uncommon" form of government. It certainly did add to that town's depth.