The only canonical pairings that I can think of all involve Leon. Leon's campaign hints heavily at him having feelings for Ada, and he also shared a kiss with Angela in Degeneration. Then there's that bonus scene in RE4 where he flirts with Hunnigan... Also the fact Ashley flirts with him in RE4, but in both instances, it goes no where.
I can't think of much beyond that. But basically, Leon is the franchise's go-to guy when romance is involved.
Leon and Chris totally have the hots for each other. I mean just look at the scene in RE6 where they fight, you can feel the sexual tension. That wasn't a fight, it was just an excuse for them to grope each other ;)