Dream list of new features:
1) Characters: Add a little role playing element with heroes, princesses and dark lords who strangle people by squeezing their forefinger with their thumb. Kidnap a princess, frame someone else, and create a diplomatic incident! Rescue the princess and divert a war!
2) Spies: I think this has been added but I'd like to see them as heroes with names and not abstract entities.
3) Government: Political parties should be more individualized, not merely a set of bonuses. I'd like to see some "evil" parties introduced, who will cause the civilization to drag over to evil alignment. And some "good" parties, just to be fair.
4) Terrorists: Not aligned with any civilization but with an extremist idealogy. You need spies to fight them, and they may even get you into wars.
5) Religion: Why not? Religion exists in the real world, why not put in the game as a force which causes effects across civilizations? Some could be "good" and some could be "evil." Civ IV has shown how this can work.
6) Random events: Starship accidents, meteor showers, earthquakes, tsunamis, solar flares, wormhole openings, plagues, famines, etc.
7) Emperor: The player is head of state, why not give him a title like Emperor, President, Satrap, Sultan, etc. Minor feature, but fun.
8) Planetary battles: I hate, hate, hate the way this is done in Gal Civ IV, which follows the same model as all other 4X games. Invasion should not necessarily be a genocide. You should invade with troops who conquer a planet and occupy it. The troops should not kill everyone on the planet and replace them. If you want to add colonists to a conquered planet you should sent colony ships. This means there should be a distinction between troops and colonists, which Gal Civ IV does not have. There should be a distinction between populations of different races, who can co-exist on the same planet.
9) Immigration: As an additional thought, people of different races should immigrate to other worlds without player control (though they can be encouraged or discouraged). Player can encourage immigration by lowering taxes or creating a good quality of life on a planet. Player can discourage immigration by creating an INS and border patrol. Player can outlaw emigration, thus creating a police state.
10) Freedom v. Oppression: Similar to "good" and "evil" but more to the point, people will want to leave oppressive planets (high taxes, poverty, police state building, propaganda) and live on free planets (low taxes, wealthy, free press and religion).
11) Specialists: Civ IV has this concept, i.e. scientists, artists, merchants, etc. These people would flock to "free" planets and leave "oppressive" planets.