Alien 3, Clu Clu Land, Ms. Pac Man, The Little Mermaid, Urusei Yatsura, The Quest of Ki, and Hello Kitty no Hanabatake have been added! I can't believe I missed some of those... As for the rest:

@Dalaamclouds, I had no idea you could choose the hero's gender in DQ III and IV! I like the equality, but for this list I only want to include games that feature an explicitly female protagonist.
@ZapRowsdower, I added Clu Clu Land and Alien 3. For Ice Climbers, Player 1 is always Popo, so it seems he's more of a main character than Nana. For Fire Emblem Gaiden, there is both a male and female main character, but it seems like you start the game as the male protagonist and the female one doesn't appear until later.
@cowboyjosh, I have never even heard of that movie or prototype! Too bad it was never released on the NES. Glad someone dumped it, I'll have to try it some time. Nice find!
@Vee - I think this list will exclude romhacks, but I cannot believe I didn't think of Ms. Pac Man...
@zn0, those are all great suggestions! Added.

Thank you all for the suggestions!