A nation-building game. Not something like Civilization, something deeper, where philosophical ideas are traded and evolve with time (resulting in vastly different mindsets and societies depending on the course of the game, NOT changing from Slavery to super-happy democracy in one year), relatively realistic relationships between States are achieved, trade and economy follows a coherent model, wars are won more on preparation and strategy than on whoever has the most units (numbers would count, just not be everything). And it would not take place on Earth (or even with humans), so that we would be free of historical bias, as much as possible anyway. Yes, I do realize it would be hell and played only by a few people, but damn I would enjoy it so much.
On the more violent side, I would like a more involving shooter experience. One where the PC is not a one-man army, but where control and maintenance of your squad would be paramount. It would have a tactical map (and, of course, non-linear levels, as much as following a story allows, think JA2 or Fallout Tactics), a pause (or a TW2 like time slow) which you could use to give orders to your mates, like scouting a specific area (the map would have a fog of war effect until it has been scouted), grenading this spot, use suppressing fire on these enemies, or defending that building. The PC would be pretty innacurate and die swiftly while confronted to many foes, forcing the player to use his or her squad. At worst, add an easy difficulty setting that tones it down and turn it into a run-off-the-mill shooter where you jump around doing headshots. The old Ghost Recon games on Xbox were the closest to that, but the aimbot AI, unability to issue advanced commands and stupid squadmates made the experience diluted.
Oh, and I would like the setting to be a low-key science fiction one, where mankind has colonized Mars but is unable to go further and faces loads of problem with violence on both Earth and the colonies (and no, none of this ''Mars rebels!!'' bullshit, this place is a rock, nothing more.)
Finally (yes, pretty sleepless these days, I am) I would like a game where the protagonist has the unique ability to ''see'' within the minds of others (no explanation, he just does). ''Normal'' people would have relatively intact minds, those troubled by something big would be rickety, and mad person would have a mess instead of a mind. The protagonist could use his talents to ''rebuild'' minds, curing mental diseases. Along the way he would face skepticism and mockery from psychologists, and what he saw would in turn trouble his mind. The fixing could be a sort of puzzle game, with multiple solutions deciding multiple outcomes with no clear best choice (do you cure a man's schizophrenia by making this or that personality completely take over? And yes this is just an example taken from Dead Money).