The common wisdom is to store all of your vegetable trimmings (cleaned) in the freezer, and then chuck everything into the stock pot when it's time to make stock. For a meat stock, it's common to throw the bones, giblets, neck and any other left-over bits into the stock pot as well.
There must be some things which are undesirable or ill-advised for stock. What should one avoid as an ingredient for making stock, and why?