In pretty much any society, the government (or lack thereof) plays a major role in how people live their lives, so it's definitely worth it to put some thought into how your world's countries/provinces/kingdoms/etc. are run.  Keep in mind that different places can have different forms of government.

Here are a few to think about:

Anarchy

-no organized central government

-if there are any positions of authority are small and temporary

Chiefdom

-regional populations are organized by a hierarchy of chiefs

Democracy

-government officials are elected by citizens

-may feature groups of like-minded individuals working toward common goals and thoughts (political parties)

Monarchy

-in an absolute monarchy, the king/queen makes all the rules

-in a constitutional monarchy, the king/queen's power is limited by law

Oligarchy

-a small group of people rule

-the rulers could be family, members of the elite, decorated military veterans, or another common thread

It's also worth it to think about your military organization.  

-Is the military run through the government, or are there only local militias?  Is there any form of military at all?  

-Does your military have multiple branches, or are the soldiers trained to handle any problem on any field?

-Do soldiers live in barracks together, or do they have separate homes?

-Can soldiers marry, or are they required to remain single until they're out?

Obviously, there is more to think about, but this is just a bit to get you started :)