I've tried to make sure there isn't a public thread already discussing this, if I've somehow missed it, do whatever you need to do.
So today I was browsing the forums, and my brain started growing possible ideas for companion quests. I don't have ideas for all of them, but hopefully this might get the idea train rolling.
Charon:
In the course of traveling with you Charon has determined that the LW is a good/honorable person and asks them to destroy his contract. I'm currently imagining this would probably be similar to the point system in place to activate Boone's quest, possible point items being activating the purifier, wrecking Paradise Falls, and helping Hannibal and the escaped slaves get to the Lincoln memorial safely.
Clover:
At some point in her time with the LW, the LW removed her collar, and unknowingly loosened her mental bonds as well. After X she asks them to help her find someone who can undo her conditioning. I'm figuring that a good karma resolution would be taking her to a doctor, though not a basic one if possible (maybe Julie Farkas?), and helping her get past the conditioning Eulogy put in place. Bad karma would probably be reinforcing the conditioning, specifying the LW as her master/mistress.
Star Paladin Cross:
Her travels with the LW have brought her to a place she's tried to avoid thinking about, Fort Independence. With the reminder right in front of her, she asks for the LW's help with reconciling with an old friend who joined the Outcasts. This idea is pretty bare-bones and is totally open for being expanded on.