I think that it behooves everyone to help the less fortunate. It does depend on what kind of help is being provided-- it doesn't help someone to simply hand them money and send them on their way. It makes more of a difference to teach them how to help themselves, but money helps where initiative and drive fail.
Yes rich nations should help poor nations. If you are lucky enough to live in a place where all is well then that is good. Now you need to care for others to ensure that we all have an equal quality of life and the same odds as you do. This include nation leaders and citizens.
First world countries have a duty to help nations in need. It may not be a legal obligation, but it is a moral one. As fellow human beings we must do all we can to help out brethren in need. Standing by and watching human suffering and not doing anything at all is not okay.
In certain instances, yes I think rich nations should help poorer nations, but I think maybe it should only be a one time thing, not help them constantly, over and over again. It's kind of like helping a person but then not expecting them to then start doing better for themselves.