While there is no couple exactly chosen within the game or movie, there seems to be some clue to this pairing. To myself, though, I believe they are a canon couple. Cloud and Tifa were childhood friends. At first, Tifa wanted nothing to do with Cloud. However, that changed when Cloud made the decision on becoming a member of SOLDIER and when Tifa made the promise. It isn't till years later that more scenes of themselves together made it that much clearer.
Now, since I haven't played the game, I cannot go based on facts within the game itself. However, by the articles and summaries, I can go by those. After Cloud is found, Tifa never leaves his side. She tries to help him through everything that happens. There even seems to be some jealousy when Aeris enters the picture. However, once more, it is not Aeris who is with Cloud through it all. It is Tifa. When Cloud is lost to the Lifestream and found by the group, it is Tifa who leaves the group and stays by Cloud's side. When Cloud falls into the Lifestream again, Tifa is with him to help peice his memories back together.
Even after the game, when Advent Children takes place, there are events that show them being a couple. Cloud leaves for he believes he cannot protect the ones he loves. Tifa wants him back in her life. She believes they have the duty of taking care of "their" children. When she wakes up during the evening, she tries talking to Cloud, making him understand that he shouldn't give up but fight. In the end, Cloud finally sees that she is still by his side, that she still cares about him and always will.
Cloud and Tifa's relationship is rough, I can admit that much. However, they are a pairing that work for each other. One will care for the other when one is lost. Another will be there when they return home. No matter what happens, I always see them together. I see how much they care and how much they will stay together.