Ideas that I don't believe I could do justice, yet I hope other authors will take up.
1) Justice League idea, Bruce Wayne raised by the Joker:
Neglectful and harsh taskmaster parents caused Bruce to reach out to the only humorous person around, the insane criminal who murdered his parents. Only rule is Bruce must be as insane as his adopted father with few if any redeeming qualities. He should not be a good guy or a dark hero. He is a villain through and through.
2) Familiar of Zero/Zero no Tsukaima idea, Louise summons a summon from Final Fantasy:
Preferably, she would summon a more humonoid one or gain the power to summon them all as needed. The only rule is that characters from Final Fantasy cannot be a major part of the story, other than the summons. Otherwise, it would probably get too convoluted and remain unfinished.
3) Justice League idea, Superman or Superboy raised by the Riddler or any other intelectual villain:
I see too many overpowered and/or paragon Superman stories. I'd like to see one where he is slightly weaker, less vulnerable (not immune) to kryptonite, and way smarter. This could easily be done in a realistic/acceptable way with superboy. Though, I'd really love to see it done with Superman before any other.