Nice and Jacuzzi from Baccano is definitely up there. I relate to Nice on a very deep level and ship the two of them so hard.
Kyoko and Sayaka from Madoka Magica have so much chemistry, and are just as great as friends. They seem to really connect.
Senri and Rima from Vampire Knight seem really in sync with each other and have a level of depth the rest of the show lacks.
Ed, Al, and Winry make a great trio with a lot of range in terms of skills and their relationships between each other.
Kirito and Sinon have much more compatibility as allies and confidantes because they share a lot of the same struggles and relate to each other most. I ship him with Leafa, but I can admit that he and Sinon would make a better pair on the overall.
Keiichi and Mion are my eternal favorite anime couple because of just how deep and spontaneous they are. I ship him with Rena too, but nothing beats him and Mion in my book.