Opposites attract, or so the cliche goes, but is there any truth in it? Research on this topic shows that they may......or may not!!! Which is hardly surprising, since it's another extremely complex issue.
Firstly, what do we mean by opposites? Are we referring to physical appearance, political/philosophical beliefs, personality, or something else altogether? Secondly, whether they are attracted to each other, and stay together (a real test of the theory?), will depend on the personality type of the individuals involved.
We generally become friendly with, and spend more time with, those who share our beliefs and values. It's usually unconscious, but most of us prefer to be with those who have a similar sense of humour, approach to life, moral code and so on. It's easier, we don't have to spend a lot of time defending or explaining our fundamental ethos, there are likely to be fewer arguments. Alternatively, it can be healthy (and interesting) to have our views challenged, because otherwise we can become smug and complacent and assume everybody sees the world in the same way we do.
Those who are secure and happy in themselves, who have a better sense of self-esteem, are going to be more secure around somebody who opposes them; the less secure individuals are going to want greater reassurance and reinforcement.
We often admire those characteristics in others which we think we lack, they are complementary, yin to our yang. However, people like Jung would say that we can only identify them because they already exist within ourselves and we have difficulty expressing them, so what we really see is that person's ability to be what we want to be. In which case, perhaps what we really find appealing is ourself, not our opposite?!