I think F-Zero and Star Fox are the ones in most desperate need of attention. I still think of these as two of Nintendo's flagship franchises, even if new games are few are far between.
Star Fox, in my mind, has the greatest potential because its more of a blank slate. The series has seen on-rails shooters, action-adventure, and even a shooter-strategy hybrid. I know many fans want the series to return to its roots -- fast-paced, on-rails, sci-fi shooting -- but I believe it could be something much more. I'm thinking a cross between the ground missions and third-person shooting mechanics of Jet Force Gemini mixed with the open-ended air missions of arcade flight games like Rogue Squadron and Crimson Skies.
Edit: I know Assault embraced a lot of these ideas, but the execution was off.