Galaxy Side Quests
Galaxy Side Quests, for lack of a better term, are quests that do not take place on any specific planet, but are driven either by your presence on the Ebon Hawk, or by your discussions with your party members as you gain experience and proceed along the main storyline. Unfortunately, the character-specific side quests seem to be unlocked only by having that character in your party a significant portion of the time; if you keep Carth on the Ebon Hawk for most of your journey, for instance, it seems like the game will be less likely to offer you his side quest later on.
To increase your chances of obtaining a character's side quest, speak to them after every time you gain a level.
Canderous
Canderous' many tales of derring-do during his time as a soldier in the Mandalorian Wars are quite entertaining: well-written, with a fantastic voice actor to back them up. The first few times you talk to him, he will regale you with stories of atmospheric entries in battle armor, combat in asteroid fields, and so on. He's not just here to amuse you, however, and eventually, you can expect him to start speaking of the end of the Mandalorian war, and how he came to live a mercenary life.
If you keep Canderous with you, he'll run into a Mandalorian named Jagy eventually, who will challenge him to a fight in the Dune Sea on Tatooine. Find Jagy and kill him to complete Canderous' quest.
Carth
Carth, in addition to being the love object of female PCs, has some pretty serious psychological problems. Unfortunately, you won't be able to drop him off at the shrink's and get him out of your hair; you are, for better or for worse, his ad hoc counselor during your voyage, and he explains in (eventually) meticulous detail the genesis of his untrusting nature. It appears that he was once a protégé of Saul Karath, erstwhile Republic admiral and now commander of the Sith fleet.
Carth's side-quest involves his long-lost son, who disappeared after his home planet was destroyed by the Sith fleet. If you unlock his quest, you'll eventually meet someone who tells Carth that his son is alive and well--and training to become a Sith at the Academy on Korriban. If you travel to Korriban and meet up with Dustil, you'll have to choose between killing him, or obtaining a datapad from Uthar's rooms and convincing Dustil of the error of his ways.
Juhani
Juhani's tale begins with the story of her journey to Dantooine, and eventually extends backwards into her past, including the story of her harsh upbringing on Taris, and the bitterness she feels towards you and Bastila regarding what she feels was your role in its destruction.
Once Juhani relates enough of her backstory, you'll run across a beast of a man named Xor, who apparently intended to buy Juhani as a slave at one point in his past. There is a pretty obvious choice during the first conversation: attack the man (Dark side) or attempt to curb Juhani's rage (Light side).
If you choose the Light side path, Xor will eventually return with a couple of Rodian thugs. He'll be easily defeated, but will still attempt to turn Juhani to the Dark side, so you'll get another chance to egg her on, or impress upon her the need to chill out. Dark side players might be disappointed to know that if you tell Juhani to kill the man, she doesn't actually move any closer to the Dark side. Your character takes a Dark side hit, sure, but Juhani immediately changes her mind about the morality of her action.