1. Change the way the techs work. At the moment it feels like 90% of techs have an effect that just adds some arbitrary percentage to a score/attribute, so it feels more like a grind and less like finding a cool new thing. No more "+10% fertility" or "slightly better laser gun" technologies. Have them do things that are distinct, interesting, and have a clear effect on the game.
Bad idea. Keep it the way it is.
2. Connected to the above, remove all the fiddly little "laser III" style weapons. Have weapons with more interesting qualities. Lots of different types of damage and effects that allow civs and the ships you create to feel more unique.
Bad idea. Kepp it the way it is.
3. Remove limitations on how many improvements can be built on a planet. Have planet quality refer only to population size, industry rate, instead (and maybe have certain improvements depend on a certain level of planet quality to build). To stop spamming of a certain improvement, have only one of each type available to build on a planet.
Bad idea. Too much like "New Game"
4. More resources, that have unique effects, and can be found in a variety of places both in space and on planets. For example a fast propulsion drive might require "unobtanium", which can only be found on certain planets. Give resources fun and scifi themed names, not the current generic ones like "influence resource".
5. Allow useful things to be done to non-habitable planets. We could build unmanned mining facilities to exploit rare resources, millitary facilities, etc etc that act to improve the habitable planets in the system. Maybe even in late game you could terraform them.
Uses for worthless planets. Good Idea.
6. Allow the construction of wormholes between systems, allowing instanteous or near-instantaneous travel between them. This will speed up combat and introduce a new dynamic to warfare - disruption of supply lines when enemy ships destroy wormhole gates to cut off distant systems from support.
Bad idea. We all know the AI would be crippled by this.
7. Connected to the above two, have a generic "worker" ship module that creates stations, mining facilities, wormhole gates, etc. These work like miners rather than constructors, i.e. they aren't "used up" when they build something.
Bad idea. Where exactly do the resources come from for the miners to use. That's why it takes time to build a construcor.
8. Have the concept of mixed populations. Currently when you conquer a planet, the native population dissapears and is replaced entirely with the soldiers. This is not only unrealistic, it implies that every single planetary invasion is accompanied with mass genocide! Instead it should track the percentage on each world that is of a certain race, and give you the option to either commit genocide, to enslave them, to give them limited rights, or to embrace them as full citizens of your empire. Depending on how you act, what the galactic situation is, and the character of the race itself (are they aggressive, freedom loving, etc?), this can have different effects. Treating them too harshly might lead to protests (that disrupt industry) or even full rebellion; however giving them too much freedom might cause the same thing. Over time, if they act peacefully and are given full rights, they become assimiliated and cease to have loyalty to their original empire. Of course, if they end up getting conquered again by their original empire, these traitors may face some harsh punishments for their lack of loyalty...
Workable idea. As in "needs work", but has potential.
9. Remove the good-evil system, instead replace it with a simple system of values or policies, i.e. slavery vs. caste system vs. egalitarianism; democracy vs. dictatorship. If you act badly, however, for example committing genocide or slavery, or using terror stars, you can still expect other civilizations to look on you poorly.
The game already works this way.
10. Minor races should be kept, but changed considerably. There should be a lot more of them, and the category should basically consist of all pre-space or pre-interstellar civilizations. They can either be exterminated, enslaved, or persuaded to join your empire (see point 8 above for possible repurcussions of this). They should provide unique bonuses that make them a strategic resource. It may even be possible for them to become a full fledged civilization given the right circumstances (e.g. a random event that has them using a salvaged ship to reverse engineer an interstellar drive).
This is already in the game in certain decisions you make when you colonize planets. Pre-industrial civs are so insignificant they don't warrent more complexity.
11. More "terrain" in space. Nebulas that slow movement (but contain valuable resources), black holes, quasers... Basically all the wonderful and varied things that science and science fiction have imagined to make up the universe should show up in game. This might also include giant space monsters that attack ships.
As long as there is a way to turn it off...