I've discussed the relation between rights and obligations before. One thing that a lot of people seem to think is that you can have responsibilities or obligations toward someone who doesn't have any right to you doing what you do. On the other hand, others thing that any obligation you have toward someone implies that they have some right to you doing it.
One thing that affects how you think of this is whether rights are explanatorily prior to obligations or the other way around. I'm not at all attracted to the view that rights are fundamental and that obligations are derivative from them, but that's a view that a lot of people have. I'm much more inclined to think my rights arise because someone has an obligation toward me.
If rights are prior to obligations, then here's a funny result. If an obligation requires that there already have been a right, then what about my responsibilities to myself? I think Immanuel Kant was right in taking us to have such obligations. If I seek a bad life for myself, that's immoral even if I don't harm anyone else in the process. If I do things that harm myself but don't affect anyone else negatively or positively, I have still done something wrong. I have violated my obligations to myself. But how can this be if every responsibility is based on a right? What right do such obligations rely on? Do I have a right to myself doing this? That's an extremely odd way of talking. Do I have a right to certain behavior on my own part?