R’ Moshe Feinstein in a T’shuva (YD 2:174) http://hebrewbooks.org/pdfpager.aspx?req=919&st=&pgnum=290, says that it is in fact a mitzva to donate an organ after death to save a life. The issue is that the organs are largely useless after complete cessation of heart function.
Many want to claim that brain stem death is Halachic death even while there is still heart function, (organs donated at this point would still be valuable). Some claim that this position was agreed to by R’ Moshe. But whether R’ Moshe actually held this position although he never wrote it clearly in a T’shuva is a matter of great controversy and is at the heart of the debate about Halachic organ donation.