Altruism can exist. Not to say all are capable. There are those whose characters are naturally manipulative and self-serving. However, I would like to point out that most people can hardly be either way all the time. We will help our grandmother because we love her. We will help a distressed friend because we can relate to their troubles. We will help a lost child because we fear the possible dangers that may come unto him if we did't help. Some people will find or hope for a reward from these type of actions, but I believe we are driven by something more powerful and much less callow- our natural ability to connect with our fellow human beings and relate to one another emotionally. This is what I believe this can power altruism and the actions practiced from its existence.
By the very definition of Altruism. That is to do the right thing and not expect anything in return. Essentially being selfless. It does not exist and can't exist. As for the majority doing good is part of a religious system. They may claim selflessness but only do so to get religious glorification.
Non religious people. They too do good but not selflessly. Doing good provides with a sense of achievement or self approval that they are a good person. To be truly altruistic. One would donate a kidney to Hitler as much as they would to Einstein. Since being altruistic is to be selfless, is to do the right thing regardless of rewards. Heck, one would donate a kidney.....Even if it will not make them feel any better about themselves or anything.
Good deeds always seem to have some sort of motivation behind them. I have yet to see a person do a good deed, which has in no way any motivation behind it. A motivation is often based on achieving an outcome.
Altruism essentially cannot exist without egoism. A pinch of egoism is always present even in the utmost altruistic person. Hence does true altruism exist? Certainly not.