Every funeral consumer (at least in Texas) should complete following legally binding notarized forms while still alive:

• Body Disposition Authorization Affidavit
• Appointment of Agent to Control Disposition of Remains

These forms ensure that your wishes are unambiguously known and that you have designated someone to carry them out.

Consider the case of Retired Gen. Hugh Robinson in Dallas.  His survivors fought for three weeks over the disposition of his remains.  It is very unlikely that he wished for his survivors to litigate the question; unfortanately there was no unambiguous expression of what he did want.  (Read the full story here.)