Sub-Quests

The Eagle

 * Searching the ship will gives clues as to the fate of the former crew.

Etti IV

 * Speak to Atton Rand near the merchants for a quest involving find which one is corrupt
 * Find Tirala in the company offices for assassination contracts. There are four.
 * Speak to the Czerka contact in the market square for a robbery quest.
 * Find the dock administrator for a quest involving deciding which passengers should get to leave.

M4-78-B

 * Speak to the two shady looking characters, in the left room near where you land to get a thieving quest
 * Find the 'spaced droid' near the factory floor for a quest involving droid romance.
 * Speak to the Czerka contact by the receptionist droid near where you land for a mission from them.

Telos

 * Speak to the Mayor for a mission involving picking his second-in-command

Coruscant

 * Shenna Rand should approach you as soon as you enter the main street for a quest about investigating Supreme Chancellor Cressa
 * Speak to General Grenn in the Senate to hunt down Iridonian Mercenaries (one is in the jedi temple, another in the slums, more will be added when found)

Mutanda

 * Speak to the shady character in the bar for a quest involving getting rid of some merchants

Character
The following characters have quests which become available after talking to them enough: You may also get HK-47 to open up to you by talking to him. There is no quest, but there is XP.
 * Tsig
 * Shadow
 * Bastila
 * Canderous

Training
After saving the Exile on Etii IV, you will have the option of visiting Freedon Nadd back at his tomb. Return to him, and he will offer to train you further. If you say you do not wish to follow the way of the Sith, you can then journey to Rhen Var. In the cave/tomb there, you will find the spirit of Ulic Qel Droma, who will train you in the ways of the Jedi.