I have found that initially I am really put out when asked to / or find myself having to do work someone else has left behind as they, usually, can't be bothered.  However, when this has happend to me, the main reason for sorting it out is that if I don't, it will only reflect badly on my boss or his department so I really had no choice.

But, I have always made a point when the work was completed of telling my boss at an appropriate moment what I have sorted out and they have always been grateful (and hopefully noted this for when they are doing my appraisals and salary reviews! )

I find myself doing odd jobs now that really are not mine to do but in doing them, someone has always commented that it is really good to have someone sort things out and thank you very much. 

To a certain extent I do feel appreciated but won't let it get to the stage when others in the office just assume I am a soft touch and will ignore things assuming I will do them.

Once I heard someone say when the copier got jammed, "oh, leave it, (me) will sort it out" - I told them in no uncertain terms that I am not the odd job person so they need to sort it out themselves.  I suppose people will always try to take advantage but hopefully the ones that matter (like bossie) will reward you for being such a model employee