1. Stealth Technology.
I think this would be really cool for the expansion. After researching (perhaps in the Sensors tree), you could put stealth modules on your ships to make them invisible to everyone, at least on the map. It would be great for freighters and transports. Additionally, stealth detection technology could be researched and also be added to your ships as modules.
2. Portal Technology.
I personally like to make my warships very powerful, and often this causes them to be very slow. There should be some way to instantly move them from one part of the map to another. I suggest a kind of "portal" technology. Perhaps this can be a starbase module. You would be able to "link" two portals together, which will allow you to move ships into one and they would appear instantly out the other.
3. Sabotage.
Similar to espionage, you should be able to fund sabotage. With enough funding you should be able to destroy another civilization's economy, morale, etc. Perhaps it can destroy planetary improvements as well.
4. Planet Destroyers.
Often, I don't want to build enough transports to take over dozens of planets. I also don't want to build influence starbases and wait for the planets to rebel. Ideally, I want a ship that could completely destroy a planet and move on. Perhaps this technology is only appropriate for evil empires, but I think it is necessary to help the game end more quickly when you have already clearly won.
5. Moving Starbases
I think this should just be available as a very late-game technology. It would be great for fully upgraded military starbases, because sometimes they just aren't where you need them to be.
- Fragsworth