Oh, I hate open questions! I very much dislike ambiguity. But ok.
If by "responsible" it is meant that our actions affect the feelings of others, then yes, to an extent. The things we do can affect the way that others feel, and the things they do can affect how we feel. But that is not always the case; it depends on the individual.
If by "responsible" it is meant that we have a personal obligation to not negatively affect the feelings of others, then the answer is both yes and no.
We should do our best to try to not hurt the feelings of others, as long as by doing so we are not hurting ourselves, or sacrificing something important.
For instance, it's best to try not to needlessly insult another person. Sometimes it may be necessary, especially if the insult is a truth that must be considered.
We should not behave in ways that are unethical. If we are behaving ethically, and the feelings of another are hurt in some way, then we are not responsible for it.
To an extent, each person is responsible for his or her own feelings. We do have some choice in the way in which we react to things. Sometimes people will overreact to something, and blame another for their negative feelings. I believe that we are responsible for using common sense and logic when dealing with different circumstances.
On the other hand, human beings do not have complete control over our feelings. If someone wrongs another in some way (such as committing infidelity, or a robbery, child abuse, etc ), then that person would be responsible for the feelings created by the action. For instance, the person who assaulted me is responsible for the negative feelings he created, however he will never have to suffer any consequences. However, it would have to be an actual wrong, not just a perceived wrong.