I've really not played that much, but there are some things that I've had in my head now and then.
1.) Captial Ship Commanders and Fleet Commanders
This has been mentioned, but I find it really cool - it'd be great to have one's own Solar Macharius, residing in the best CAP, conquering entire systems.. and such a weeping when loosing the beloved admiral!
2.) Drop ships and boarding
Certain ships should have ship-to-ground and ship-to-ship boarding abilities, e.g. sending troops onto planets could give a chance to 'destroy' and instantly capture it, depending on the level of the boarding units. This would work similiar with ship-to-ship, maybe with the boarding units inflicting massive damage if successful.
3.) More diverse tech trees
The player should be able to really choose a path in the tech trees, building a militarily, economically or culturally strong empire. These paths should feel different depending on the chosen race.
4.) Being able to fortify choke holds, even when they are not colonizable
I've often had a tactically priceless choke hold on my maps, a needle eye for the enemy. Holding this point would give an immense advantage. Sadly, these are mostly gas giants and asteroid belts. It'd be great to be able to build defensive structures, i.e. an inhibitor and a repairing bay here.
Space Stations would be a great option for this role. Placed inside the gravity well and having an immense firing range as well as power, creating a barrier the enemy would have to pass.
5.) Being able to fortify or 'shut down' worm holes
Maybe this isn't that great, but it'd be an option. Give players the option to collapse worm holes. This could be really costly, but would grant security.
6.) Make defending viable
Right now, only the AI is a viable target for defenses. Players mostly just ignore them, so they aren't even built any more.
I, for example, like having a good defense up. I like to fortify nearly all of my planets - but I know that players would just sweep it away.
Make defending viable, so that a player can be successful with both offensive and defensive strategies when used correctly. Maybe Gauss cannons could be upgraded or another type of orbit weapon added.
It'd be great if a well-defended world could hold its own against a small to larger-than-average pirate raid or a player's small fleet.
7.) More and better commands for fleets
In my opinion, most ships behave quite well in combat. Sometimes, though, it'd be great to have been able to give certain commands before a fight, e.g. 'stay back and support' or 'guard / assist that ship / these ships'.
This would be being able to choose a political system for one's empire - examples have been given -, giving certain boni and mali.
Maybe a player could interact with a neutral world when having the 'right' system or use political pressure to capture the world.
9.) Add a screen for the player to quickly view the last few actions and commands for his empire.
10.) After increasing the bounty, there should be a small break before the pirats start their raid. Sometimes, it all comes down to who had the lucky last click.