After completing the last class quest (about level 16) on your second planet you will receive your ship.

**Planet: Dromund Kaas**

 - Imperial Agent will receive a spaceship after completing the quest- Cleaning Up the Mess
 - Sith Inquisitor will receive a spaceship after completing the quest – In The Halls Of Traitors
 - Sith Warrior will receive a spaceship after completing the quest – Leaving Dromund Kaas
 - Bounty Hunter will receive a spaceship after completing the quest – Joy Ride


**Planet: Coruscant**


 - Jedi Consular will receive a spaceship after completing the quest-
       Ancient Secrets
 - Trooper will receive a spaceship after completing
       the quest – Assault On The Works
 - Smuggler will receive a spaceship after completing the quest – Race the Devil
 - Jedi Knight will receive a spaceship after completing the quest – Race to the Ruins

[Source][1]


  [1]: http://www.swtor-spy.com/guides/how-to-get-and-upgrade-your-starship-in-swtor/190/