Puppet regimes are of tremendous importance, espescially when it comes to conquer, colonize, or having an imperialist policy.
Maybe something simplistic can be included without trouble (and still give a gross picture). For example, if you instaure a puppet regime on a conquered planet, it will:
- Have a lower unrest and/or cultural change possibility than a blatantly conquered city
- A part of its production will go to you (metropolis)
- A part of its production will go to its formal owner (in form of money, trade, whattever)
The potentiality of unrest will slowly diminish if you maintain a calm situation and give what the inhabitants want.
I read that one of Paradox' games (Victoria: http://www.paradoxplaza.com/victoria.asp) has puppet regimes, but I never played it.
Edit: By puppet states, I mean states with hidden strings, implicit limits of sovereignty, oriented towards a direction to start with, etc. All possibilities.