Strong: Do they have to be the protagonists? Cause there are some pretty strong bad gal characters in the Metal Gear Solid series (Fortune and Sniper Wolf come to mind). Samus Aran, Chell, Alyx Vance, Jill Valentine are strong, but have already been mentioned several times. I always liked Helena from the Dead or Alive series (just the fighting game, not the slutty volleyball games). Helena was an opera singer who fought to avenge her mother's death. That's pretty cool.
Weakest: Princess Peach of course is the epitome of melodrama cliches (I can just picture her tied to the railroad tracks by Snydley Whiplash (sp?). Princess Daisy is not much better...her voice makes me cringe. Going back to Metal Gear...Rose. *feels the need to bang head on table recalling Rose and Raiden's banter*. Tina Armstrong from the DOA series: she fights for the opportunity to dress like a slut despite daddy's wishes? Kitana/Jade/Mileenea from Mortal Kombat series were pretty disappointing. Same slutty outfit, just different colors.