I'm going to say... Qualified No, people do things that border on unselfishness. Here is why.
1- Having kids, inherently unselfish (personal level). Having kids doesn't benefit you personally in the long run. You are still going to die. You don't get to transfer your soul into the husk of your children when you die. If you could, then it could be construed directly selfish. But the fact is, no matter how many copies of your DNA you put into this world, YOU don't get to benefit from it directly. When you're dead, you're dead and that's the end of your self. Maybe the act of creating the children was totally selfish because it feels good, but many people go beyond that, actively putting effort into their children. Maybe our children will take care of us in our old age and maybe they won't. Even if it feels good to take care of our children, we still die someday and won't be fully repaid for our "unselfish" efforts.
2- Situations where helping others costs trivially more than not helping them. Situations where "I lose nothing and somebody else gains something." If I'm driving to work, and someone lives very nearby to me, I might let them car pool with me. Their weight will only add a few pennies of cost since most of the cost is the car pulling its own weight. I lose next to nothing, they gain something. Maybe they throw in a few bucks for gas and maybe they don't. Even in the grenade situation, where there isn't time to throw the grenade back. I'm dead either way. Having my comrades die too doesn't make me LESS dead. So, since I'm a goner anyway, why NOT throw my body over the grenade and try to soak up some of the blast. I lose nothing that I wasn't going to lose anyway, and maybe I save some of them.
3- Evolutionary effectiveness. Wolves working together can bring down bigger buffalo and eat where single wolves would starve. Pack and hive structures exist throughout nature (bees, ants, chimps, bird and fish flocks, every social animal). The pack strategy is by working together we can survive better than working on our own. Sometimes the pack helps us (parenting, pack protection), sometimes we help others or lay down our lives or at least some of our food for the pack. Humans are no different. We are the children of parents who worked with the human tribe rather than went it totally alone. As such, we are not total loners and not dedicated totally to the self. We aren't just "self-ish", but we are more "self or pack-ish". Now, helping the pack IS generally good for the self, but as I said sometimes we sacrifice for the pack. That's the trade off! Seeing it this way is seeing ourselves as something more- what is good for us is good for the pack, what is good for the pack is probably good for us (but might be bad for us personally- when we sacrifice for the greater whole.)
