Anybody who says promiscuity is nature's way is a fool. As an early disclaimer, my analysis of this situation deals with primitive man. Please do not think I'm being sexist with future comments and take into account that modern conveniences allow humans to do a lot that, by our natural abilities alone, we couldn't do. That being said...
One of the main reasons that we see long-term, monogamous-type relationships in certain animals usually stems from the evolutionary need to have a partnership in ensuring the survival of the offspring. In humans, the whole cycle takes around 9 months and is quite debilitating for the female. If the man didn't stick around to help feed and protect his mate, then, chances are, she would die. This doesn't result in the survival of anything, let alone your genes. Age to maturation also plays an effect. It takes human beings about 13 years to mature to the point where they would be viable on their own, and that's even a stretch. A family unit forms a core of protection during pre-maturity.
I wouldn't go so far as to say that monogamy is evolution's way, but it definitely causes some long-term relationship biases in certain animals. Elephants are a good example of this as well. Penguins find long-term mates as well because of the intense burden the caring of young would be on an individual. I think that people who claim that sleeping around is our instinct are taking too broad of liberty with what they see on the Nature Channel. What applies for some doesn't apply to all, and, if you haven't realized it, humans are a pretty unique animal.
In addition, humans have identified that, as a group, we are far more capable than as individuals. This bias towards grouping up affects a lot of our psychological drives, seeking a monogamous relationship as a long-term connection (typically resulting in a family group) is just one. Trying to get a potential lover into your "in-group" has a strange effect. The time spent courting often results in a sense of familiarity, eventually leading to security, and finally to dependence. This security reaches the tribal part of our brain's urge to collectivize. Unrelated, this is also the reason why anarchy is a joke of a mythos. If no government existed, people would form along family, tribal, or community lines in order for survival.
I could go on for pages about social and evolutionary reasons why long-term relationships work well for humans, but I'm done here....for now....