Couples come together for a number of reasons: circumstance, chemistry, lust, passion, necessity, convenience. But the reasons they stay a couple are based on how well they complement each other. There are many lenses through which to evaluate your compatibility with your partner.
Your values are what matters most to you in life, the driving force behind your life, and what motivates you when make decisions. For this reason, successful partners generally share many fundamental values. If your core values are very different and there is not a lot of overlap, a relationship will likely not last. If you value financial security, material abundance, fun and leisure above all things, while your partner most values deep friendships, world peace, hard work, and minimalism, it's hard to imagine why you were even drawn together in the first place. But as they say, sometimes opposites attract.
Hobbies and Interests
Partners should be able to have fun together, and so should share a fair amount of things that both would consider fun. While you don't have to share all of your hobbies, a little overlap is necessary. You may not understand your girlfriend's obsession with Anime, and she's not at all keen on your library of silent films, but as long as you can find some things that you both consider fun and enjoyable, you can make it work.
Partners should have compatible personalities. For example, if one is incredibly shy and withholding while the other is very outgoing and demonstrative, they run the risk of feeling misunderstood by each other, or having poor communication. Another duality, the extravert gets her energy by being around others, while the introvert is more restored and inspired by time spent alone. This dynamic may make it hard for them to agree upon how they will spend their leisure time together.
Goals and Dreams
While not necessary for a short-term relationship, a long-term commitment requires that you have similar goals or visions for your life. If he wants to live on a cattle ranch in Utah and have eight kids and you have your eye on a penthouse sweet in New York and a childless life, you will either need to be willing to make some serious compromises for each other, or you may need to reconsider spending your life with this person.
Despite all the other evidence pointing to relationship bliss, if he is in a band touring Asia for two years and you are an elementary school teacher in Hoboken, your situations are very different. Shared experience in necessary for a relationship to thrive. While you may be compatible as individuals, your situations are incompatible. Some couples will tough it out though, as long as they know the situation is only temporary.
There is a school of thought that the order in which your are born in relation to your siblings affects your personality as you develop. In general, relationships where the partners include one youngest sibling and one oldest sibling are most compatible, because the older one naturally takes on the role of leader, while the younger is generally more passive. If two oldest children get together, they may butt heads because both are used to always getting their way and being boss. Meanwhile, two youngest siblings are often so passive that a decision can't be made between them.