Well I have played though a couple of games and I have some thoughts on what I would like changed.

The galaxy

1 Purple and Green stars, there are no purple and green stars. How about you make those into Binary star systems, no planets, Purple/green star systems never have habitable planets anyway. (or just make the purple ones binarys and make the green ones into yellow stars)
2 Red stars, Again these never have habitable systems so make them into red giants (3-4x bigger) with one gas giant planet.
3 Orange stars, these also have no habitable planets, make them 1-1/2x bigger then a yellow star and add the possibility of a lesser planet being in orbit, like a mars planet but never an earth planet.
4 Blue\white planets should be 1/2 the size and only have ice worlds around them. There should be a chance that one of the worlds could end up being habitable, though very small like 5 tiles.
5 Your homeplanet, should always be a 20+ planet and you should not have to research to unlock tiles. All tiles should be workable from day one, you have been there thousands of years. All earth type planets should have a large amount of tiles IMO
6 Mars type planets, they should all have no workable tiles until you research and unlock thoses tiles.
7 I would like to see planets a bit further out from the stars and have the sectors much larger so the stars are more spread out. Make all the maps larger to compensate.
8 Black holes, Nebulas and other spacial anomolies in the game. Have the odd nebula inbetween stars and make them affect sensors and shields, so ships could hide in them.
9 Allow ships to orbit uninhabital planets. A thought I have on this is that if you put a ship in orbit it will become invisable to everyone else, the only way to spot ships in orbit would be through spying or if you have a ship right beside the planet. Of course the AI would need to be able to utilize this feature. IMO this would really bring those planets into the game.
10 Moons, radomize the starting location of their orbits. ATM all the moons orbits are identical, same speed is not a problem, just that they are all at the same place in orbit at the same time.


Improvements

1 The need to build an improvement on a planet to enable orbital fleets has got to go in the worst way, this is just a plain bad idea.
2 Space stations, this just ends up a logistical nightmare. Make it so you only need a constructor to build the initial station, then have the station able to build its own upgrades for cash, but do not make it instant, the upgrade should take time.
3 Space station ship yards, ability to create spacestations that can build and upgrade ships. I havent thought this one through much but they should be a huge undertaking, being able to move ship production off-planet thus freeing up planet tiles for other things would be a huge benefit.

Ships and upgrades

1 This is currently IMO a bad set up. My thought is that not all parts should be able to be put on all hulls. Put limitations on what parts can go on certain hulls. So large hulls would not be affected they can have any part, but a tiny hull would not be allowed to have photon torpedoes and warp engines for example.
2 In the ship yard there should be a list to see obsolete ships.
3 Upgrading ships, this should have to be done on a station or planet and it should take more time, you should not be able to instantly upgrade ships in the middle of space. Also if you make this change (makes it harder to upgrade ships) lower the cost up upgrading ships.
4 Stacked ships, ships in orbit. I should not have to seperate ships from planets other ships and spacestations to give them orders. Currently It is impossible to park a ship on a space station and commend it to sentry.
5 Add a ship order to sleep, sometimes I park a sensor ship and I do not want it wakeing up every time another ship flys by.
6 To be able to set up patrols would be nice.

I think thats about it, probably forgot some things, I'll add to it later.
Feedback welcome, what do you all think of my ideas.