Check out this great article from Positive Parenting Skills on teaching responsibility.
Kids are adverse to responsibility as north is to the south pole. They have learned from an early age that others will take care of them, feed them, bathe them, dress them. It is no big shock that responsibility is something we have to teach them because they are not born with it. So we must train and coach them in this arena.
It doesn’t help matters that responsibilities are normally B-O-R-I-N-G!! And we know that kids love to do exciting things. Cleaning their room or doing dishes are not stimulating for them, period. You could get creative in these activities and try to make them more interesting, however visions of broken dishes and clothes hanging from the ceiling fan do come to mind!