I always liked fations in X-Com Apocalypse. Having rival organizations spawning around the globe like X-Com but with less resources would be so awesome... A diplomacy feature would also be cool. Hard to implement, I know but one can always dream.
Reasons for them spawning could be the following:
-Not satisfied enough with X-Com performance: Most likely a faction made of the country's military forces or a private X-Com like organization if it's at least 2 countries one next to another. They will only be active in their territory.
-Totally influenced by alien activity: Free alien base for the country also containing human/hybrid soldiers.
-No longer influenced by aliens: Not really an organization, if X-Com destroys the country's bases provided by aliens and all its military forces, the country will succumb into anarchy, no longer being able to be influenced by any faction. Any Tactical mission in their territory will contain hostile gangs of humans and hybrids that will attack anyone that isn't one of them.
-Ignored UFO crash sites: Secret organization not friendly with X-Com but attacking all UFO crash sites to recover alien tech for their own ends.
-High alien activity Low X-Com activity: Secret worldwide X-Com like organization neutral to X-Com.
-Selling equipment that doesn't need Elirium: A major [Sold Item] manufacturer that will considerably decrease selling prices but will also allow you to buy that item.