I tend to side with Thomas Hobbes on the inclinations of man, being that if man were left to his own devices life would be "nasty, brutish, and short". I believe that, fundamentally, humans will act in their own interests over those of others. A person who believes that killing is morally wrong, for example, may kill someone in self defense.
This isn't truely a question about morality, for morality is dictated by those who have power. For example, morality for Muslims is much different than morality for Christians. On the same token, good and evil all depend on which side of the story you happen to side with. No one is TRUELY neutral (you hear me Switzerland? lol).
In the end, it's not that mankind is good or bad; it's that we are self serving. "good" and "bad" are concepts created by societies we live in and are not relative to what we are as a species in the long run. You don't call an eagle bad for killing a fish to feed themselves; you don't call the fish good for being killed - it's just how things work. The only reason we can say that humans are good or bad is because we've risen above the funadementals of life - we (for the most part) don't focus on surviving; we strive to make life better with technology, education, and the arts.
Our DNA DOES dictate somewhat how we function as a person, and this does change from person to person. Testosterone being the hormone of aggression, males are typically more aggressive than females. Those males who have an extra chromosome (XYY, also known as supermales) are overly aggressive and violent. This makes a great case for genetics dominating who we are; but can't completely cancel out the nurture side in the nature vs. nurture debate. Just because you're born with genetics doesn't mean you will turn out a certain way - it just means you're more likely to.
In the end though, man is truely moral-less. We are born tabla rasa (clean slate) and from there our moral code is written upon us by our parents, friends, and culture we live in. Since no person is born in a vacuum, free of any and all influence, it's impossible to avoid being morally slanted to a certain viewpoint. It's important to remember that morals are just that though, a viewpoint - a way to interpret life, a code of conduct, and a way to separate right from wrong.
Ultimately, there are two ways to answer this question. Firstly, if you're speaking of man in the nature state - devoid of all culture, governments, and social groups, much like man in an animal state, then no, man would have no "morals" and would act out of impulse with an emphasis on the self over others. In modern society however, man is not naturally good or evil - all men are, in a way, neutral. For what I in the United States may view as Good, someone in Afghanistan may view as evil - this doesn't make either one of us right, it just makes us different.