As a lover of political fantasy, I also love creating governments. There are so many things to play with, so many ways to create something different, interesting, or filled with possibilities. The main thing I try to remember that every system is made up of the interaction of smaller systems.
For every government there is at least one revolution--which may or may not be "righteous," and may or may not be successful, or even all that active--and within every governing body, there are individual agendas. What these are and how they will react to a given stimulus depends on their makeup, beliefs and environment.
So, once I've decide what kind of government I want to write about, I consider what kind of culture I want to write. In Born of This Soil, I decided that the Pyrani would be a plutocracy, ruled by the wealthiest members of society. These would be the Merchant Prince/sses, and they would be in charge of exporting the nation's products and importing what the nation needs. Each tier of society is divided up by wealth and serves a specific purpose in the nation's economy.
Artists made up the poorest category, but because the Pyrani have a great appreciation for art in all its forms, artists are absolved from the plutocratic caste system. Regardless of how much they make--and some of them can become quite wealthy under the financial support of rich patrons--they are always immune to the responsibilities (such as taxes, community involvement, etc.) that the Pyrani associate with greater wealth and greater status. However, this also means that those labeled "artists" are also forever outside the mainstream of the Pyrani society. It's this twist in their government which ultimately allows them to create some of the conflict they do in the book.
There are many different types of governments. Monarchy is far from the only option (as much as us fantasy types love those kings and queens). Even within a monarchy there is room for loads of variation. Consider how you want the government to function, who you want to be dissatisfied with it, and how large a part it plays in your story.
Even if you're not writing a political fantasy, politics can fill in gaps in the plot, can deepen characterization, and give your world depth. Think about how much the politics of where you live affect your life on a daily basis. Most of us think of politics as something huge, something that deals with the needs of an entire nation, but these things have smaller ripple effects throughout a society.
You can find a list of different types of governments with a quick Google search. The point is not what system you choose, but how you blend it into the species, plot, and world that you've created. That's what's going to make it different, interesting, and fun to read. After all, I don't want an explanation of the parliamentary system; I want to see how it affects your characters lives.
I build every government which has even a chance of making it near the plot. I do this because I feel that it gives me access to details I might not even realize I need until later down the line. You can always worldbuild the basic. Write your first draft. Building anything else you realize you need. Edit. Worldbuild again, and so forth, but having the world laid out in front of me lets me add in things I don't need for the plot, but I need for the culture, the feel, the mood, the themes, the imagery, the symbolism, etc. Sometimes, if you don't have that to hand, it doesn't get put in at all.
So, consider how your characters (and species in general) feel about the government. What do they like about it? What do they dislike about it? How much of it is invisible to them because they can't see how it affects their lives? In SFF, governments tend to have a strong and visible effect on the characters' lives, but there are always blind spots.
The more you think about the government's effect on your characters, and the more you include characters with varying opinions of the government, the more fleshed out your government will feel to the reader. And, the deeper your characters will feel.