The answer to this question depends sensitively on the precise definition of ego, and each of us may be using a different definition. To approach the question from a top-down perspective, everything we do is motivated by some process within our minds. If you look at a person as a system, they have some input (sensory perception) and some output (speech and behavior), and the output is a function of the input. If you define the entire range of this function as ego, than by definition, all behavior is egoistic. Otherwise, all behavior is not egoistic.
This argument is trivial, but the real question is, when we debate whether or not all behavior is egoistic, are we really conveying any more information than is contained in this trivial argument? We certainly think we are, but I'm not so sure. I'll give the debate a try anyway. :p
I read about a grand tournament wherein a slew of programs designed by different computer scientists took turns playing against each other for many iterations of the prisoners' dilemma. Each program kept track of its total score throughout the tournament, and each program used a different strategy with regard to its opponent's behavior on past iterations. The surprising part is, the most duplicitous, backstabbing programs did not win the tournament. The group of programs that scored the highest had several rules in common.
1) Tit for tat. You scratch my back, I'll scratch yours, you hurt me, I'll hurt you.
2) Benefit of the doubt. I'll begin by scratching your back, and see what you do.
3) Second chances. Sometimes after you hurt me, I'll still scratch your back, and maybe you'll change your tune. (Sometimes better to risk giving you more points and not getting any back, than to risk getting locked into a pissing contest for the rest of our iterations and never getting any points.)
Remember, these are simple computer programs, with no thoughts or motivations, just hard-coded rules to follow, despite my anthropomorphic portrayals of them. The interesting thing is that without any concept of self-interest or altruism, it is an empirical fact that the "trusting, forgiving" programs made out better than the ones that followed a purely "selfish" strategy.
Well, we're programs, and evolution coded our rules, and our rules are called instincts. Our points are surviving offspring. We're the products of natural selection for the highest-scoring rules, which include our instinctive altruism. The key word is "instinctive" - for many, many generations, we had no concept of ethics or morality, we simply felt like helping each other (because for many, many generations, those with a tendency to feel this way via random genetic mutations scored more surviving offspring.) Today, in addition to our ethics and morality (and sometimes in spite of them), we still feel like helping each other, much as we feel like screwing each other, much as we feel "fight or flight" when something scares us, etc.
Much as we feel like looking out for our own interests. Self-interest is an evolutionary strategy also. You need to survive to mate, and to take care of your offspring. But your genes don't care about you, your genes only care about your offspring. More precisely, your genes only care about your offspring's offspring. Even more precisely, your genes only care about your genes. More precisely still, as simple chemicals, your genes don't have the ability to care about anything - they're simply the ones that got replicated because they're good at getting themselves replicated, using you as a carrier.
My point is, even without any intellectual belief or justification whatsoever, you'd still have altruism. However, the reason for this is because you've evolved that instinct as a survival strategy. So, does that mean altruism is egoistically motivated?