2 Way Tie!
Sten and Shale from Dragon Age: Origins. They bond over their contempt of humanity. It’s rather adorable.
The other spot belongs, oddly enough, to Master Chief and Cortana. It was never something expressly explored in the series but there was a nice connection between the green armored Spartan and pink glowing lady. I was smiling pretty hard after retrieving Cortana in Halo 3.
Runners Up: Shepherd/Garrus (ME2, Romantic/Bromantic), Joker/Normandy (ME2), Locke/Celes (FFVI), Gordan Freeman/Alex Vance (HL2)