My feeling on this is that I am clearly responsible for recycling those things that I am able to recycle. However, I do not feel a responsibility to save things that my city does not recycle and then bring them somewhere else to recycle.
I do feel that I have a responsibility to recycle everything that I can. I think that it is irresponsible to waste things. On this earth, we have limited resources. Everything that I use and throw away is something that will not be available for my descendants to use some day in the future. In other words, it is somewhat selfish to throw things away when it is not necessary to do so. I would be, in essence, saying that I do not care enough about my descendants to go to the bother of recycling something rather than throwing it away.
However, I do think that I have to be reasonable about what I expect my responsibility to be. I do not feel a responsibility to drive a long way to recycle things that my city does not recycle. I do not feel the responsibility to abstain from buying anything that cannot be recycled.
Overall, I do feel the responsibility to recycle as much as I am able to recycle with a reasonable amount of effort.