Thanks. Added.

sin and punishment is a legitimate nintnedo frnachise

It's developed and owned by an fully independent company. It clearly is not a Nintendo franchise.

It is developed by Treasure, but do you have anything to prove that they own it?

On Treasure's site at the entry for Sin and Punishment there is "(C) 2000 Nintendo". I believe that means Nintendo owns it.

You're forgetting several franchises like

Rhythm Heaven, Style Savvy, Mach Rider, Trace Memory, Electroplankton, Picross, Clu Clu Land and others.

Some nitpicking but where's Pokemon Platinum?

Some more nitpicking but what's Nintenod?

EDIT: If you can divide the Mario sports games from the platformers, RPG's, etc, where's Pokemon Ranger, Mystery Dungeon, Ranch, etc.

This applies to some games that are in the list already, as well as the bolded ones, but I don't think that one game makes a franchise.

Um, yes to all except Trace Memory (I see no evidence of Nintendo ownership) and Picross (I's a common game anyway, Nintendo hardly own it.) I'll add them in a bit.

Nintenod is me writing half the title and accidentally hitting the submit button. Should be "State of Nintendo's franchises on Wii and DS".

I'm sure Style Savvy will have future installments.

As for Mach Rider, I  see your point.

There is a Mario Sports game on the DS--3-on-3 Basketball or something. There are also Final Fantasy characters in it XD

Mario Hoops 3-on-3?