Does altruism exist? Or perhaps I should ask, "What exactly is altruism?" The accepted definition of altruism is the state of the holding of someone else's interests above one's own or, when when that state is put in practice, doing something without any reward or expectation of reward. Taken strictly, however, I think that this definition of altruism defines something that may not exist at all.
The problem lies with the concept of reward. While most people will associate reward with some sort of monetary or material gain, a more robust approach would be to associate reward with utility, and monetary and material gain is but a subset of all possible forms of utility.
If the beneficiary is someone with whom there will be future interactions, there could be the reward of reciprocity, either in the form of friendship or the knowledge that the beneficiary may be more inclined to help in the future. In a religious context, believers of a personal deity would be rewarded by the knowledge that the deity in which they believe in approves of their action (and whatever other additional rewards are associated with that approval). Finally, and most importantly, an expression of gratitude from a beneficiary can also be considered as a reward. Even if the beneficiary does not explicitly expresses gratitude, there is still satisfaction that can be derived from implicit gratitude.
I would like to pay special attention to the concept of the reward of implicit gratitude, because I would like to argue that this is a reward that is always expected. By definition, people will perform an "altruistic" act if they believe that the act will somehow benefit the beneficiary (altruism is about intent, so whether or not it really benefits the beneficiary is irrelevant). If this belief did not exist, then the act will be malicious act. However, the belief that the beneficiary will benefit necessitates, by definition, that there be implicit gratitude, as implicit gratitude is simply the beneficiary's internal appreciation of being better off. The beneficiary may not even know who the benefactor is or the beneficiary may refuse to explicitly express that gratitude (and thus earn the label of "ungrateful"), but those sorts of considerations only affect whether or not there is explicit gratitude, not whether or not there is implicit gratitude. I thus maintain that there is always, at the very least, an expectation of implicit gratitude when a benefactor does something for a beneficiary, even if the benefactor expects no material gain, no explicit expressions of gratitude or even if the benefactor remains anonymous and unknown to the beneficiary. Or to put it another way, there is always a reward of the knowledge of doing something good, and this is a product not necessarily of society, but of the naturally-evolved human empathy that everyone is born with.
For people who object that these sorts of non-tangible rewards are not really rewards, I remind them that what people ultimately seek is utility, and as such, money and material goods are not an ends, but a means. Money is a means to goods and services, and goods and services are a means to utility. As a result, there is no good reason to preclude other sources of utility.
As a result, I think that altruism in its strictest definition does not exist in the same way that Euclidean lines and massless pulleys do not exist. At this point, you are probably thinking that this entire post has so far been nothing more than a frivolous exercise of semantic quibbling. After all, what matters to most people is what the vernacular definition is, which is doing something without material or monetary reward or in some uses of the word, without the reward of explicit gratitude. So what does it matter what altruism means in this strict context of considering all possible rewards?
There are some cases where imprecision and muddling of definitions can lead to confusion and even to elaborate arguments and belief systems built upon a mistake of semantics. I speak of Ayn Rand's objectivism and its vitriolic attack against altruism. Rand believes that acting in a way that is entirely devoid of reward is immoral. If altruism is defined in the strictest sense, then this is a point that I would have to agree with by default since this is a form of altruism that is a priori impossible. However, objectivists, in a logical impropriety, then apply this argument to a looser, more vernacular definition of altruism. If it were not for this semantic muddle, objectivists would be forced to defend their attack against vernacular altruism by somehow invalidating the utility derived from non-explicit means, and I suspect that they would have had a much harder time at that.
PS: There are many other cases where semantic imprecision can be exploited in rhetoric. For example, some theists argue that atheists are hypocritical about faith because in order to say conclusively that there is no God requires an atheist to make a blind leap of faith. This is true, and this is also why pure atheists in the strictest definition are probably very few in number, if they even exist at all. Even the most radical "atheists" are technically agnostics; they do not know for sure that there is no God, but they think that the probability of such is so low that they effectively behave as though none exists, and they call themselves "atheists" only because the vernacular definition includes atheist-leaning agnostics. I suppose the message that I would like to get across is that semantic precision is a lot more important than most people think it is.