DmC Dante x Kat, even though they were platonic in the game. I'd just really want that couple to work considering how much Kat opened Dante's eyes to the world and gave him someone to trust.
I would ship DmC Vergil x Kat, but Vergil was a selfish manipulator with her. I guess I'd ship them if Vergil actually cared about her.
Classic Vergil...I guess I'd have him on his own. He didn't show any interest in Lady, and I doubt he has interest for relationships anyway considering how driven by his plans he becomes. Plus, he just seems too cold and distant, not to mention violent, for the duration of the game.
I wouldn't mind seeing Lady x Dante, but I think their partnership is more business orientated, especially considering how Lady becomes in the anime and DMC4.
As for cack ships that make no sense:
Mundus x Lilith. I suppose I ship them because of the headcannon dynamic I have between them; how she's really into him, constantly trying to please him, and using the baby to get his power and favour, while he doesn't give a flying fig about her so long as she gives him what he wants. I just find their relationship interesting as it's nuanced and a great example of what a relationship should never be like.