More historical guidance to have nations do what they do historically while still allowing them to do what they want (Frankly, sounds like this is already in the works, so yeay to that.)
More options for "alternate history" nations like Granada, Ireland, or an England that has taken over half of France that now has to be more involved in the Continent and thus changes the dynamic for the region.
Easter Eggs. C'Mon devs, hide your initials on a coastline somewhere, or make one of the advisors look like you. Also fun things, like on xmas, your king puts on a santa hat or something.
A scenario editor. PLEASE! Simple clicks to create a base for our scenarios. Something "Paradox Approved" and even if it is DLC with a pricetag, something that has technical support.
Faster Fast. Allow us to tone down the graphical interface as much as possible (IE political mapmode makes trees vanish or whatever) so that our games, when set for "Fast" go "Faster". I want my game to run like a jet engine, let me skip from 1450 to 1550 in no time flat.
More music. Better music too, EU III music is great, don't get me wrong, I think it's amazing, but damn it I'm greedy, blow my BLEEPing mind. Lets all be honest, when we heard Civ IV's Baba Yetu, we all had chils, and we still get them all these years later. I want that and more!
Modability out the wazoo. Let us make 2 HRE's if we want to and a Papacy for each religion. Maybe I want each country to have factions, some have 2, some have 20, and others change between the two.
Keep all the great features a lot of the other posters want to eliminate like balanced gameplay designed provinces, wasteland, hard missions, no "Making things like CK or Vic" just make them great!
No more ping pong! If I want ping pong I'll play ping pong. This is the most annoying aspect of the entire game really! Make an army unable to retreat to a province it's retreated from within the past little while.
A game for the ages. EU III lasted quite a while, and so have many other big titles, and part of the reason is there has not been much in the way of "revolutionary" change to strategy games during this period. Make EU IV like Sim City IV, make it last for a decade if it needs to (by allowing it to be extremely modable to players and developers) and don't make an EU V until there is a reason to update the series.
Less dependence on continents. As it stands, if you are in Europe, you suffer similar drawbacks to provinces you own in Morocco, Egypt, and Natal. Change that so that "nearby" areas of other continents don't punish you as much as "Far" regions of those continents. IE if the region is on the 'edge' of a continent, it is considered to be only 'half as far' or something from the neighbouring area. IE Russia would be 'closer' to Asia than Germany, France, Spain, etc etc.
Let us do anything with cheat codes. We should be able to rise and/or lower just about anything we want with cheat codes. If I want less colonists I should be able to do that with a simple command. If needed, make events that do this. Don't be afraid to make events where the only possible trigger is though the console.
And last but not least: Random Americas. This is an idea that I took from a variant of the game Diplomacy. In short, Europe, Asia, and Africa will be as they always are, and, the distance between China and Spain (across the americas) is fixed. What is different is what is in between. Have the "Americas" be randomly generated. It's a bit 'unfair' that we are humans - who generally know what the world looks like - do not share in the wonder of discovery. Make us discover new world by creating them. Allow this to be an option, you can either play with "Normal" Americas, or with "Random" Americas.