A great idea. Maybe one of these poll wise people will make it so.
It'd need to be for just for main/prominent recurring characters, no one-off guest appeances, otherwise you'd have huge lists and would most likely forget someone that would cause outrage.
Going by that, here is the list I can think of:
TOS: Chapel, Rand, Uhura
TNG: Crusher, Guinan, Pulaski, Ro, D. Troi, L. Troi, Yar
DS9: E. Dax, J. Dax, Kira, Leeta, Winn, Ziyal
VOY: Janeway, Kes, Seska, Seven, Torres, S. Wildman
ENT: Cutler, Sato, T'Pol