I think that «отказ от прав» is very clumsy and «предупреждение» didn't cupture the sence thought even here (https://russian.stackexchange.com/) it used widely in cases where second choice is more appropriate.
The Wikipedia article that Clever Masha referenced, reads that disclaimer is widely used in US including every day life situations. However it is well known that russian culture is not used to legal terms in every day life. I think that we have to separate situations when disclaimer is used by companies and when it is used elsewhere.
So, when publishing house, software company or cinema studio uses disclaimer it is translated as legal notice. All examples below are typical "заявления об отказе от ответственности":
Издательство не несет ответственности и не предоставляет гарантий в связи с публикацией фактов, данных, результатов и другой информации.
Редакция не несёт ответственности за содержание авторских материалов.
Все персонажи являются вымышленными и любое совпадение с реально живущими или жившими людьми случайно.
When disclaimer is used in other situations it is not common to Russian culture. The example that you are giving "Disclaimer: J. K. Rowling owns Harry Potter, and no one owns the methods of rationality." references both legal and "non-legal" sphere, so it is hard to find adequate translation immediately. This disclaimer references fantasy setting of the book, so to translate it one should try to find some creative solution. In this case "предупреждение" seems not so bad, but definetely looses 'legal' feeling of the term.
(It worth to note that Multitran also lists "юридическое предупреждение" as invention of cell phone provider MTC. Here 'legal' background is back).
Update 2 New idea came to me 3 years since the original question. Предуведомление sounds quite old-fashioned and bureaucratic, so, to my mind, it combines both legal (like "заявление", "особое мнение", "извещение", etc.) and fantasy setting (since it is old and not so widely used nowadays like предупреждение).
If I understand correctly "disclaimer" is not widely used in russian law, so the translators usually are trying to find the appropriate existing russian terms in different fields of knowledge (business, software, telecommunications, cinema, etc.). This is typical situation with freshly borrowed terms.
So, the translation depends on context.
I think that most general translation is "отказ от ответственности". I think this is the best translation for the software EULA, where they write "The end user uses this free software 'as is'".
However in the movies when they state that all the characters are fictional the translation may be "оговорка о случайном характере совпадений".
More official "corporate style" translation may be "заявление об отказе от ответственности".
However in patents and in jurisprudence (legal practice) there may be more appropriate translations in different situations: правовая оговорка, защитительная оговорка, отказ от прав, отказ от изобретения, дискламация элемента товарного знака, etc.
See more alternative translations on Multitran.ru
We call it simply "дисклеймер". Wikipedia also confirms it.