All non-main companions. Every class only gets one companion who actually gives quests. Usually it's the first companion, but for the Jedi Knight it's Kira, who's your second companion. May be the second or third companion for other storylines too, I haven't played them all yet.
It's a little annoying, because every companion has obvious hooks for quests. Like "I gotta go to Taris to rough a dude up!" *fade to black* "OK, back from Taris!" Because it's not like I wanted to go to Taris with you and help out with that.... While they're adding s/s to companions, maybe they can finish that too. A comprehensive "companion patch" that offers universal storyline extras on top of s/s fixes would certainly be a good way to garner the interest and support of folks who are otherwise indifferent to or uninterested in just the s/s aspect.
I had the impression that originally it was planned that you would accompany the companions on these quests, why else do they always take place on planets you have already visited in the past. I think that BioWare simply ran out of time and or money to do them right and so all the player gets are those fade to black.