I would like to see the following:
1. mine control centers:
Give each grav well 10 mine tactical slots. For each slot you can place 1 mine control center, which can control 10 mines in its space of influence. As those control centers are cloaked the enemy can't see them. The only ship which does not trigger those mines are the scouts. Once a mine control center is detected by a scout, the center can be targeted and destroyed, which would also destroy the mines in its influence. This would make the clearing of a conquered grav well much more reasonble and the mines still deadly (espeacially if two mines could kill a cap...). In order to avoid mine spam in each grav well of the map, especially early in the game (which would slow down game speed considerably... You would have to clear each grav well befory you can jump to the next one... That would be really bad...) those mine control centers can only be placed in one's own cultural influence.
There might even be a reasearch option, that star bases can use the mine control centers as long range detectors, using their long range weaponry in the region of influence of a mine control center. That way a star base could cover a whole grav well.
2. Mother ship:
The mother of all ships. Make it four times the size of a cap ship. Each race can control only one of those ships at a time. It should be able to take care of two caps easily, however it would sustain extra damage from strike craft (they are too fast for the point defense system of the mother ship... huh, memories of star wars...) and to siege frigates.
What would really make them cool, would be to have four tactical slots for them. You can add some special system to the mother ship, which would benefit the ship or the whole fleet (high accuracy targeting: gives each ship in the fleet 10% more damage, fast phase lane computing: decreases the jump time into phase space, extra point defense: takes out strike craft faster, frigate factory: well, produces frigates, extra shields: imagine the shield generator in star wars, etc...). However you can only fit four special modules on this mother ship. Those modules have their own hit points and can be destroyed. It must be easier to destroy them than the whole mother ship. Additionally, one could refit the mother ship at the mother ship factory, exchanging those modules for a price. The different modules should be researchable.
3. ramming speed:
If a cap ship has lost 2/3 of it's hit points, you can select an enemy cap ship as a target, press a button and your heavily damaged cap ship accelerates to ramming speed. If it reaches it's target it explodes and substracts it's remaining hitpoints from the enemy cap ship. That means, you can still deal a desperate blow, without it being too overpowering to turn the tide in battle. It would just give you the amount of time needed to rescue the rest of your fleet by fleeing. (or to destroy the retreating level 10 Marza, you nearly have finished off...)
4. Drop ships:
Give them the possibility to drop on a planet and capture it and it's infrastructure. These would be single use ships and need to be rebuild. You will need a 3:1 ratio (compared to the planets population) if you want to conquere a planet (additional research can lower this ratio, like personal shields, dropable hover tanks etc.). As conquering a whole planet intact is highly desireable, it needs to be difficult, too. For example: Drop ships are only build for speed and don't have any weaponry. A planetary defense is researchable which uses some kind of flak only damaging dropships, thus decreasing the likelyhood of success for the invader etc... (Those drop ships should also reflect the distinct species, like vasari having a hive ship, which splits into 10 little ships before falling onto a planet etc...)
Those drop ships might also be used as boarding ships after a research...
5. Boarding parties:
Use ships to board enemy caps. You need a certain amount of boarding parties to indeed capture a whole ship. If you use less, then the target will only be a bit less effective (less damage...) because the crew is busy fighint the invaders. Once a ship has been captured, it can be scuttled for resources or being brought to a research facility. After a time it can be used for your own fleet (the distinct possibilities needs to be researchable...)
6. Ship formations:
Next to just looking cool, they should have certain effects. For example: "vic formation" on strike craft: lesser damage output but higher armor value (strike crafts are covering each other), claw formation: bonus for frigates against cap ships, but penalty against strike craft, etc... Well, this would need ships to actually move in battle...
7. Admirals, Diplomats and Traders:
Being able to build a school of advanced tactics. This will give you (depending on your research and species) the possibility to hire one admiral, one diplomat and one trader. Those hero characters give a special boost, which is upgradeable by research. They need to be placed and can be killed. The admiral will have to be placed on any ship and will have -of course- military benefits for the fleet he commands. The diplomat will have special spying and negotiating skills (as negotiating with another human player is rather difficult, this diplomat needs to have a given set of abilities: like you negotiate with an enemy and automatically receive 100 credits from his income. He can be used once in five minutes, or sth similair... You might be able to target an enemy structure and then this building is 5 % less effective due to a computer virus... etc.). The trader, then needs to be put on a star base and boosts your economy, depending on research. As a "Hero" character is being created by the media, those characters are only functional in ones own cultural influence.
8. Political systems:
It has been mentioned by others already: Let's have a deeper focus on politics in this game. Political systems should be usable, which will have effects (both positive and negative) on trade, military production, research, cultural influence and negotiation.
9. Spying centers:
Cloaked structures, which can be build in any grav well. They are detectable only by scout ships. In it, the spying abilities can be researched and used, affecting the surrounding grav wells.
10. There have been a lot of cool thoughts already mentioned by the others...
Just my thoughts...