We are first and foremost responsible for our own selves. After all, if we don't take responsiblity for meeting our own needs, can we reasonably expect someone else to do it? We should not expect to meet our needs at someone else's expense, though, unless it is unavoidable, as when we hurt an attacker while trying to defend ourselves. At best, we can help others as we meet our own needs.
Our next responsibility is to our family. Again, if we don't do this, who do we expect will? Some relatives won't need or want help. Some might get help from friends or other non-relatives. But barring serious estrangement or abuse situations, we should help them when they need it. On a par with this is close friends or a SO. If we enter a relationship by choice, we should hold up our end of it by caring for the other person and being there when they need us.
More broadly, we owe everyone at large two things. (1) To care for the world we all live in, and behave as a responsible neighbor, coworker, citizen, etc. This includes things like not wasting resources, cleaning up our messes, following the rules/laws that smooth daily interactions, etc. (2) Treating everyone with a basic level of respect and civility. Yes, we owe this even to difficult people or outright jerks. We can (usually) draw the line without acting like jerks ourselves. If we do violate (1) or (2), it should be for a damned good reason, and we should be ready to face the consequences.
