We know from Wesley Hohfeld that one person's possession of a right implies duties on the part of others. My property right regarding a bike implies that everyone else has duties to let me use it how I so choose, and not to use it themselves unless I have given them permission.
People sometimes talk about a right to privacy. I'm inclined to disbelieve in such a right, on the grounds of the duties it must imply. Suppose I have a right to privacy concerning an affair I have had. That implies a duty on the part of other people not to talk about the affair. In other words, it's a limitation on other people's free speech. Unless they have promised not to talk about the affair, I would not believe in such a duty.
For this reason, my inclination in the recent Gawker vs. Hulk Hogan case is to support Gawker's right to publish the video. They ought not to have done so, sure, but we should be very concerned about the law acting to punish them for this. Not because Gawker itself is worthy of defending - it most certainly isn't - but because government overreach must always be stopped at the first hurdle, before it can become tyranny.
That said, I think there may be an actual case for Hogan here, relying not on a right to privacy but on sexual consent law. Consider that consent to a sexual act is generally not taken to apply merely to the commission of the act in question, but also to the way it is performed. Julian Assange is currently hiding in the Ecuadorian embassy in order to dodge prosecution for rape; the claim is not that his alleged victim did not consent to sex, but that she did not consent to sex-without-a-condom. It used to be the case that women could sue men who promised them marriage, slept with them, and then abandoned them. A few years back, a man was imprisoned for rape by deception in Israel after it turned out he was not as Jewish as he had pretended to a woman before sleeping with her.
There are a variety of things which, if not revealed prior to sex, can cause any consent to the sex to become invalid. STIs are a familiar example; I would presume that being filmed is another. Hulk Hogan was not, I believe, aware that we was being filmed; it seems fair to assume that had he known that the resulting video would be made public, he would not have engaged in the sex act in question. This would imply that his sexual partner, and Gawker through their complicity, have engaged in rape.
"Rape" is a far-ranging term, of course, and not all rapes are equally bad. On a scale of one to ten, where Gilles de Rais is something around an 8 and Amnon somewhere in the region of 5-6, Hulk Hogan's story can't be worse than a 1.5. But there's definitely a case there.