Here is a little idea that I just had:
Your civ has gone through a long, drawn out war. You didn't gain any significant land in the war, and many of your units died. One day you get the message
"The terrible war-mongering tyrant [insert name here] has been pushed off a cliff by angry peasants. They have elected a new leader [chose name], who is going to put a stop to this war-mongering nonsense, and devote his time into research and happines."
And suddenly, your civ has become scientific and religious. It could of course also be the opposite. After giving in to too many A.I. demands for money/techs/luxuries you could be reached by the message:
"Too late the weak ruler [inser name] has realized that the nobility has been plotting against him for years. They are tired of the way he has brought shame to the once feared empire of [insert country name]. They have taken control by a military coup, and has elected general [cose name] as their new leader. He will once again strike fear into the hearts of our arch enemies."
And now your civ has become militaristic and expansionist.
By using this system, the player would still always be in charge of his empire, but couldn't push the people around any way he pleases without consecuenses.
Anyway, this was just an idea, and perhaps a bad one too. I just realized that as soon as people figured out what they needed to do to have a leader overthrown, they would just exploit it (like going on wars they know they will lose so they can become religious or something like that)