Personally, I'm a big fan of
Tropico. You play El Presidente of a tiny Latin American island nation in the Caribbean, and you have just come to power in the midst of the Cold War. Now, you have to run your island, balance the varying political pressures, and shape everything toward what you want to do with your country.
You can either establish a free, open democracy by reliably standing for reelection, or you can hold to power by engaging in electoral fraud, or you could just do away with democracy altogether and run a military junta. You can pursue a capitalist or communist course of economic development, in turn influencing your foreign policy with the USA and the USSR. You can be secular in your government, or introduce religion in a more direct manner.
The game has a good premise, and on top of that, has a great tongue-in-cheek sense of humor about its subject matter. I recommend it.