Slornie is more or less correct, but I'll give some more specifics. Each faction has their standard starbase, then you have some additional slots for those buildings, the amount of which vary from planet to planet, as do what you can build there. For example, you'd have more slots on Kuat than on Dantooine. The options you have for those slots vary between factions:
Empire:
Shipyards- Light Frigate, Heavy Frigate, Capital, Heavy Capital
Defence- Golan I, Golan II, Golan III
Other- Scanners
Rebellion:
Shipyards- Light Frigate, Heavy Frigate, Capital
Defence- XQ5 (We're only including one kind because all six XQs are basically the same thing)
Other- Scanners
Empire of the Hand:
Shipyards- Light Frigate, Heavy Frigate, Capital, Heavy Capital
Defence- Four "confidential" platforms
Other- Scanners
Obviously, you wouldn't be able to build everything everywhere. Golan Is, XQ5s, one of the EotH platforms, scanners and Light frigate shipyards are the only things able to be built everywhere.