Definitely Dawn and Ash.
"Pokemon reflect the feelings of that of their trainers." Dawn and Ash's pokemon were extremely close, like a huge and very diverse family. You can definitely tell that no matter what Ash/Dawn did, the other was always making sure to cheer them on and comfort them after a loss. The high-fives, the last episode, the partner battles, Pikachu and Piplup...although I do not ship this pairing AT ALL, I believe they had the best chemistry, and think that their friendship was one of the strongest and most special within the entire show.