[AJC]

I agree the cloaked spy satellites work well - you can keep tabs on all the systems you dont inhabit.

In combat -I find satellites are only worthwhile if they are sporting seekers and/or PDC for defense of a planet from your opponents seekers and fighters.

I rarely build a base other than as repair facilities on the front lines, usually just space stations. They can also act as my resupply base when I dont have a planet nearby- just join up with them as a fleet.
I also use them when I build ring worlds and dyson spheres.
Occasionally I will build the symbolic "I built one" battle ready star base.