It's a widely accepted view in medical ethics that doctors should not do anything to patients without their informed consent. (There are some exceptions, of course, for patients unable to consent, e.g. minors or the unconscious.) A patient's consent is not binding, because they cannot force a doctor to treat them, but their non-consent is, in the sense that if they refuse a treatment the doctor is not permitted to administer it.
Yesterday I was completing a reference form for a former student hoping to go to graduate study when I read this: "Please tick here if you do not consent for us to disclose the information provided in this reference, to the applicant. If requested by the individual to release this information, we will take your consent preference into account when considering all of the circumstances and deciding if it is appropriate."
It struck me as interesting that, in this case, an explicit refusal of consent was taken as something to be considered, but not as binding. Of course, what's at stake in the two cases (medical treatment and privacy) is different. Some universities do allow applicants to waive any right to see their references, but the referee's wish not to have their comments disclosed to the candidate is (in almost all circumstances) less important than someone's wish not to be operated on.
In the case of organ donation, someone's organs can (under current UK law/practice) be used without their consent, since their next of kin can make the decision after their death. Families rarely go against the recorded wishes of the deceased, where these are known, but since many people do not make their preferences known, it's inevitable that some will have their organs used though they would not have wanted this.
This is one reason why those who do not wish their organs to be used might support a switch to an opt-out donor system: though it imposes upon them the burden of registering their wishes, it allows them to record their objection (which arguably should then be binding, whatever the views of their next-of-kin).