I have often wished, especially in light of the advanced government system that Geoffrey has in Antimatter, that Aurora had some sort of government system that you could select. You could choose from the vague standards of authoritarian, democratic/parliamentarian, monarchic/imperial, and oligarchic. Each would have customizable government departments that provide certain bonuses that diminish based on sector distance. The democratic ones would have elections and a bicameral congress (senate from planets, representatives from population). Oligarchic would have a selection process for some sort of triumvirate or whatever.
Each would, of course, have it's benefits and drawbacks. Authoritarian and monarchic governments would maybe have reduced loyalty (e.g. much higher demand for PPV and garrisons), while democratic and oligarchic would require approval of certain actions (such as declaring war, political parties that you must appease by meeting their demands, etc.). Unhappy pops would rebel and form a new empire of their own design. Meanwhile, Authoritarian might have an increase in certain types of labor, while democratic might have improved financial and perhaps things like throughput of spaceports and the like.
Obviously, I haven't fully thought it out. It's just something I'd like to see at some point.