I think it is a very, very difficult question to know when one is acting responsibly. Responsibility is something many people avoid, and at the same time, it is often a strange kind of excuse for other things. I know certain people who are always doing things for others, but don't really manage to be productive and happy, and one has the sense that they are avoiding facing the question of what to do with their own lives by being a martyr of sorts, always allowing their time to be used by others. At the same time, the world is so full of irresponsible people, people who can't be bothered to recycle a plastic bottle, who cannot see two feet beyond their own nose or consider their effect on the larger universe. How does one go about deciding what one's responsibilities are and how to best fulfill them -- quite a complicated issue.

Leah, your question gives two very nice examples, of personal and general responsibility. We have obligations to other people, which are often easier to see though they may not be easy to fulfill; and we have obligations to our larger society, which are often much less emotionally fraught but at the same time, somehow easier to ignore.

I am tempted to fall back on the etymology of the word, "response-able," we are responsible for something when a direct action of ours can affect it for the better. It is not an issue of feeling or of sentiment, but rather one of action. Responsibility has to do with our obligation to act in the correct way.  At any particular moment if we are acting in a certain way we are obviously not, then, doing something else, so the question of responsibility has to do with deciding what is most crucial, it is thus somehow always bound up with choosing one alternative over others.

It seems to me "responsibility" really only comes up in the shadow of danger -- I wonder why?

To the April 11 NY Times opinion column by Frank Rich entitled "No One is to Blame for Anything", contending that Alan Greenspan should "take" responsibility for the financial meltdown instead of offering the (false) excuse that no one could have foreseen it (actually, many did), a reader comment posted a link leading here.
In this context, "taking" responsibility refers to a mistake already made--a mistake that yielded seriously damaging consequences. But is it possible to avoid "taking" responsibility for the making of a mistake by "being" responsible in the first place?
Actually, it is. By applying information that has been available for thousands of years--predating all religion and philosophy--you learn how to "be" responsible, which in turn leads to the discovery that as long as you are attentive (the information also teaches how to be attentive) you will find that being responsible comes automatically and is therefore effortless. Not only that, but joyful.
For instance, you understand that no matter what is bothering you, when you meet people for the first time you automatically realize that they had nothing to do with it and will greet them with a smile--not just because you have decided that this is the right thing to do since they are human beings just like you--but because you have so internalized what you have learned that having to make a decision is obviated.
Unless you are attacked in some way you will walk with a smile everywhere you go, seeing each day as an opportunity to make another person better off for having encountered you.

Leah, I don't think people are motivated by responsibility at all. I think people tell themselves this to justify their actions. I am not cynical about humanity; I just don't believe people are motivated by abstractions.

For instance, your friend who cares for her abusive mother. It is easier for her to believe she's making a sacrifice and taking responsibility rather than simply following her own needs or weaknesses or insecurities, whatever they are. We make sacrifices all the time that are not really sacrifices because on some level we gain more from giving than we would have had we not made the sacrifice.

Responsibility is a neutral term than can be used to justify taking life as well as saving life, torturing people as well as caring for them. The woman who just sent her seven year old adopted son back to Russia, like a defective appliance, because she thought he was dangerous, no doubt believed she was acting responsibly. All terrorists claim to be acting responsibly, and to be making a sacrifice. And so on.

You ask, "What responsibilities do we owe in life?" and "...why do we sacrifice?" To the first, every vested interest or institution owes its existence to telling people what their responsibilities are. So be careful who you ask! For myself, I like to use a golf course metaphor and strive to leave the place in better condition than when I found it.

As for why we sacrifice, I generally don't think we do. I think we follow our needs and our natures and often call it 'sacrifice.' That's not to say, however, that self-interest is a bad thing, especially when it serves others.