This is a great idea for a game jam! And it can be a bad idea in terms of theme or mechanics:
1) 50 Shades of Grey- nothing sexual, that's just the palette you have to use.
2) Rebellious Hero- your character constantly ignores your input, or delays their actions, or does something else altogether.
3) Lost in Translation- a text-based game (VN, choose your own adventure, point n click etc.) where the text is fed into different languages in Google Translate repeatedly until it barely makes sense when it returns to English.
4) Jack of all Trades Jam- all the art and graphics have to be hand drawn by the coder and scanned in, and all the audio recorded from their own voice. Ideally this should be a solodev jam, but small teams are ok so long as nobody with any drawing, voice acting or singing talent joins the team. Any dialogue must also be written by someone who hasn't even attempted to write a story, poem or article since they were forced to in school.
5) Diplomatic Solution Jam- Sure, Mario may be fun, but wouldn't it be better if the representatives of Bowser and the princess got around a table and discussed a future for the Mushroom Kingdom that was acceptable to all parties? Similarly, instead of all the mindless violence in Doom, maybe their differences should be settled peacefully by the UN? Unleash your inner bureaucrat with Diplomatic Solution Jam...