Depending on the technology and size and the function(s) the ship was designed for a starship might have some or all of these things. Obviously there is overlap between rooms and systems in some areas but I'll stick these in categories anyway:
Rooms: Bridge, Crew quarters, Passenger quarters, Cryogenic / Freezer tubes for 'long term passenger storage', Conference rooms, Galleys, Dining halls, Recreation rooms, Sick bays / Hospital, Brigs, Plant rooms (power plant), Fuel tankage, Vehicle bays, Docking bays (different from vehicle bays in that docking vehicles remain outside the ship), Airlocks, Missile / other ammo loading bays / storage, Possibly more than one engine room (FTL drives plus maneuvering drives), Damage control centers, Science labs, Workshops (or factory facilities if the ship is really large), Cargo bays, Hydroponics (for food production)...
Systems: Power, Communications (internal and external), Sensors (internal and external, passive and active), Navigation, Life Support, Weapons, Sheilds, Stealth (Cloaking, Emissions masking) Artificial Gravity (or rotating sections for that centrifugal gravity effect), FTL drives, Maneuvering drives, Decompression control (airtight hatches to isolate breached sections, possibly autorepairing hull systems), Internal transportation (if the ship is really big)...
That's all I can think of for now... plus if a ship is really big you can go overboard on the recreation facilities... cinemas, discos, skating rinks, sports arenas, anything else you can imagine...