An idea I commented a while back. It could be with any companion/Doctor combo but I've always loved 10/Martha and wish there had been more time for Martha to shine.

I have this idea for a 10/Martha story. There isn't really a plot, as such, rather a general premise.
The Doctor wakes up in a cell in one of the Shadow Proclamation's intergalactic prisons. There is nothing he can do about his situation. He doesn't have his sonic or even his normal outfit. He's there in the typical prison get up. He has no idea why he has been arrested but is in solitary confinement. He knows he has done something really bad.
Martha, on the other hand, wakes up in an empty Tardis. She assumes the Doctor has gone off for a walk or something. So she gets dressed and leaves to find him. Lo and behold she sees multiple newscasts stating that the mass-murderer and killer of that planet's king, The Doctor, has been caught and could be placed on death row.
The plot is then mainly Doctor-lite as Martha manages to find the lawyer team tasked to defend the Doctor and together they save him and help find he's innocent. Of course he was framed... by who? I haven't decided.
It's inspired by shows like How To Get Away With Murder and takes that kind of approach to an episode. I just think a Doctor Who crime drama episode would be really cool. I also think this idea could translate to any Doctor and Companion.