Bowser
Seriously, this guy is Mario's arch nemesis and yet he's one of the only major long running Mario characters at this point that has yet to truly branch out into his own game. I mean sure, we have games that are focused on Bowser such as Mario & Luigi: Bowser's Inside Story, but we don't really have a Bowser game in the vein of Super Princess Peach, Luigi's Mansion, Yoshi's Island or Wario Land/Ware where Bowser and his minions are the starring roles and that sucks, because the RPGs clearly shows that there is a lot of potential to not only Bowser, but his kingdom as well and I want a game that focuses exclusively on that. Have us take over kingdoms, create and rule over the Koopa army, build airships and tanks, set up traps for Mario, there is so much you can do here and yet, the idea of Bowser being the star has barely been explored outside of M&L: BiS.
Hell, AlphaDream would be the perfect developers for it, since they in particular seem to be interested in Bowser too (Considering BiS has a huge focus on Bowser as well as the side stories in the remakes focusing on aspects of Bowser's kingdom), so maybe let them do a proper Bowser game or something.
Because, seriously, there is a shit ton of potential to one and I want to see that potential realized.
Beyond him though, I don't know if this counts since Kirby is more 2nd party then 1st party, but I think Dedede and Meta Knight could do well in their own individual spin off adventures as well.
I mean, why not? They already have their own playable adventures in the Kirby games via stuff like Meta Knightmare in Nightmare in Dreamland, Super Star Ultra and Planet Robobot and Dedede Tour in Triple Deluxe, so why not take that and make proper full fledged games with original levels and idea designed around their characteristics and abilities specifically.
Hell, considering Hal Laboratory loves their spin offs and has even expanded upon a few sub games into their own individual games, i'm kind of surprised we hadn't gotten this yet.