Sonic Shipping, Logically Speaking; VectorXVanilla
So, despite having two game characters, this ship is covered only by the exceptions clause. I think you might have gathered why this one might be controversial...
Characters involved: Vector the Crocodile and Vanilla the Rabbit.
Most well known nickname: Vecnilla.
Original date of ship: 2005...or whenever episode 39 of Sonic X aired.
Analysis of chemistry (aka why people do/don't ship it): In Sonic X, Vector is infatuated with Vanilla. While Vanilla doesn't explicitly return the affection, Vector still goes out of his way to help her, for a bit of affectionate gratitude. Like Chaream, it works on the poor, rough man/ neat, rich woman dynamic, which again is a Titanic in the making. They spoke a few times throughout season, but it was mainly limited because the Chaotix themselves didn't appear often.
Personal Opinion: Neutral. Vanilla's a cool mom, I'm chill with her.
Likelihood in the games: As it stands, none.
It comes under the exception clause because there's no evidence of it in the games, it's purely a product of Sonic X at this time. They have never been in a game together for starters, and thus have had no on-screen interaction. Besides that, Vanilla wouldn't exactly appreciate what he puts her daughter through. In Sonic Heroes, Vector's willing to fight her and her team to kidnap a chao on behalf of who he knows to be Dr. Eggman (although he doesn't know any of team Rose at the time). And in the only other game where the two really interact, Sonic Free Riders, while being on better terms with each other, Vector is in it solely for the money and is willing to just leave her and Amy behind once he gets it (which he doesn't. Poor him). Cream even explicitly mentions that her mother is watching her, and Vector doesn't change that view in the slightest. His interest is in business only.