if you consciously decide to give your life to save someone else, isn't the other option always worse? Are we saving a loved one because of our love for that person, because of our principles ... or because we couldn't bear a life without this precious person (and a life of blaming ourselves)?

According to research that has been done in this specific area, one of the most popular explanations for this is the one of the reproductive fitness.
A guy called Hamilton constructed a theory about this in 1964. This theory was constructed with Darwin's "survival of the fittest theory" as a basis.
Hamilton stated that kin selection can account for altruistic acts towards those who are genetically related to the do-gooder. It would 'pay' an individual (in terms of reproductive fitness) to die if in doing so a number of close relatives would live and reproduce. This is because the genes responsible for such altruistic behaviour are also likely to reside in the bodies of close relatives. Sacrificing oneself to save four siblings would pay greatly in terms of gene survival : since the genetic relatedness of siblings averages 50%, two genes would be saved for the price of one. To equate the loss of genes from a relative's death, more relatives must be saved than the reciprocal of the coefficient of genetic relatedness. (e.g. 1,5 = 2).
Such behaviors are therefor selected for because they benefit the performer's kin.Such kin selection accounts for, among other things, the high degree of altruism and self-sacrifice shown by parents towards offspring in both animals and humans.
Kin selection does not however explain why a human might do an altruistic act towards a stranger. That answer lies in the theory of reciprocal altruism, which says that it pays the individual to help save a stranger if the stranger will reciprocate this help in the future and save the life of the altruist. This assumes that the cost/benefit ratio is appropriate, that individuals are capable of recognising each other in the future and that they are likely to meet again. Of course, this strategy can give itself rise to "cheating"; acceptance of acts of altruism from others, but failing to reciprocate in the future.
In any case the individual is often placed in the dilemma whether to cooperate or whether to cheat. This was nicely illustrated by the game "the prisoners dilemma", but that would lead me too far. If somebody is actually interested in this then I will explain this game. It's quite fun actually.