Some basic ships in Star Trek:
Starfleet: Constitution Class, Excelsior Class, Ambassador Class, Galaxy Class, Sovereign Class, Intrepid Class, Defiant Class, NX class, Nova Class, Olympic Class, There are tons more for Starfleet.
Borg: Cube variant 1, Class 4 tactical cube.
Romulan Star Empire: Bird of Prey (Based on a Klingon design), D7, D'deridex Class, Drone ship, Romulan Science ship, Romulan Scout, Romulan Shuttle, Valdore Class.
There are many more ships for many more different factions, This is a pick and mix of ships.