Heero Yuy. Duo Maxwell. Pilot 01 and Pilot 02. 
This , to me, is the most likely coupling of Heero. I can't personally see him go as well with any of the cast. However, I understand there are people who disagree, claiming there is little evidence for Heero and Duo's relationship. I'm gonna have to agree. There's is little evidence. But there is some! Heero and Duo are always together, much like 2 other pilots that I will mention later (on their page) and Duo wonders about Heero . He worries about him more than the others, especially when he goes to save Relena (can you say jealous much?) and Heero, like he can't kill Relena, can't kill Duo. Duo and Heero make a great team. Maybe that's not much evidence, but if you watch the series, it just seems, to me at least, right that they should be together. 

(by the way for those who care, that picture to the right is official. I have decided to put only official pictures up unless I can't find them. That's official.)