I think that deep down, everyone is even a little selfish. Even those who do things selflessly get pleasure from what they're doing, meaning they're selfishly making themselves feel good. I think this all stems from our very nature - that as early man, of course people had to be selfish, to ensure their own safety and survival as a species.
I think by nature we are both of these but first and foremost we are selfish. It comes down to survival on the most basic level. If it comes down to survival I will be selfish and most people would when it comes to food or water. However, we are all altruistic as well.
Yes, I believe humans are selfish by nature. When you see children playing, you are seeing humans true natures. A child at day care may have a box of toys in their lap, but they always want the one toy that another child has. Children seldom share, whether its toys or candy. We are the same as adults. Our wants are what motivate us and we seldom notice the difficulties our neighbors may be going through.
We human beings have an interesting method of promoting the advancement of our species. In some ways, we can be selfish to move ourselves up the social ladder. Other times, we are generous so that we can help the rest of the species. In reality, we are a species of mutualists. By this, I mean that we typically trade off with one another to get what we need to further ourselves and others. For example, I (hypothetically) live alone in a fairly large house, and find myself needing someone to help me maintain it. Enter a grad student, fresh out of college with little money and no home. He comes across an ad I put out offering shelter and pay to help me maintain my home. We both mutually benefit from this as he gets money and a place to stay and I have someone to help me with my home. That may be a very modern example, but others can be used to explain our mutualist nature just as well (e.G. Olden days of trading a basket of eggs for a jug of milk). We work together for our own benefit and the benefit of others, this is how many agreements are reached in societies throughout history.
It is fair to think of man as a selfish being. However, the way the human society is design and built to ensure that man stays together, it is clear to everyone who follows the societal path that sacrifices are to be made every now and then. This means that to be a part of the society, an individual will act in a particular manner to follow the customs of the community he belongs to or not do certain things which are seen as taboo even though he has strong desires to do the same and it would gratify him to a large extent. The human society understands that man is willing to sacrifice for the greater good and thus puts these restrictions. Thus, man is both selfish and altruistic at the same time
It is clear from history that humans are by their nature selfish and evil. Given the choice, most people would act to help themselves alone rather than others. It is only because of the social contract that people are forced to be civil to each other and cooperate at times.