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

You will recive a space ship after the following quest:

Planet: Dromund Kaas

• Imperial Agent - Cleaning Up the Mess
• Sith Inquisitor – In The Halls Of Traitors
• Sith Warrior – Leaving Dromund Kaas
• Bounty Hunter – Joy Ride

Planet: Coruscant

• Jedi Consular - Ancient Secrets
• Trooper – Assault On The Works
• Smuggler – Race the Devil
• Jedi Knight – Race to the Ruins

Source

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

You will recive a space ship after the following quest:

Planet: Dromund Kaas

• Imperial Agent - Cleaning Up the Mess
• Sith Inquisitor – In The Halls Of Traitors
• Sith Warrior – Leaving Dromund Kaas
• Bounty Hunter – Joy Ride

Planet: Coruscant

• Jedi Consular - Ancient Secrets
• Trooper – Assault On The Works
• Smuggler – Race the Devil
• Jedi Knight – Race to the Ruins

The ship you receive depends on your class:

Jedi Knight & Jedi Consular – Corellian Defender

Smuggler – Corellian XS Stock Light Freighter

Trooper – Rendili Hyperworks BT-7 Thunderclap

Sith Warror & Sith Inquisitor – Fury-Class Imperial Interceptor

Imperial Agent – X-70b-Phantom Prototype

Bounty Hunter – D5-Mantis

Source and official site

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

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

You will recive a space ship after the following quest:

Planet: Dromund Kaas

• Imperial Agent - Cleaning Up the Mess
• Sith Inquisitor – In The Halls Of Traitors
• Sith Warrior – Leaving Dromund Kaas
• Bounty Hunter – Joy Ride

Planet: Coruscant

• Jedi Consular - Ancient Secrets
• Trooper – Assault On The Works
• Smuggler – Race the Devil
• Jedi Knight – Race to the Ruins

Source