1: Wormhole Generator, (Stargate, etc.), build one and you can teleport your ships from any starbase equipped with one to any other starbase equipped with one.
2: Really Long Range Sensors.
3: Jamming Device that blocks other civs sensors in the effected area (effectively cloaking the base and any ships in the area).
4: Death Star Laser, takes a while to charge up and recharge also very expensive.
5: Engines. Going with the Death Star concept again here, throw some engines on the base and your starbase effectively turns into the slowest but most powerful ship in the game, a mobile command center, or a mobile mining facility depending on how you've got it rigged up.
6: Stasis Field. Basically an "Oh Shit!" button, if you get invaded by a large force you can activate the stasis field and it freezes everything in the area for 10 turns giving you a chance to bring in reinforcements. Enemy ships, your ships, the base, any planets in the area and any ships that try to enter the area while the field is active will all get frozen until the effect ends. Once activated it takes a long time to recharge.
7: Black Hole Generator, destroys the base when activated as well as anything else in the effected area and creates a permanent obstacle to the movement of ships through the area.
8: Repair module for rapidly repairing starships.
9: Drone/Probe Factory, lets you build recon probes and small attack drones at a starbase.
10: Mind Control Ray, basically a cultural weapon. Lets you brainwash an enemy ship to temporarily obey you. Upgrading the ray lets it affect larger ships, more ships, last longer etc.