Tom Bell and Glenn Whitman have engaged in an interesting debate over to what extent intellectual property rights conflict with tangible property rights, and to what extent intellectual property rights, like tangible property rights, are natural rights.
Roughly speaking, Bell defines natural rights as those rights that would emerge in a "state of nature," i.e. in the absence of government law enforcement. Bell correctly observes that real and personal property rights would emerge, but argues that at least generally intellectual property rights would not. I think this is only partially true.
One poster responds with the example of symbols of office or other social status (jewelry, seals, feathers, etc.) that exist in all civilizations and most neolithic and hunter-gatherer tribes. I'd add that in England, at least, offices themselves were property rights. Indeed, English feudal and royal titles have followed for at least centuries the same inheritance rules as those for real property, and were categorized in common law as property (Blackstone described this well). Furthermore, trademark emerged in the common law, suggesting it would also emerge in the absence of the state. Academic norms of anti-plagiarism are a form of IP-like rights that we can observe today being enforced outside of government. The Domain Name System (DNS) on the Internet, and the related Internet Protocol address space, were enforced without the formal legal recognition of rights in these areas long before the DNS was discovered by the government legal system. Indeed, title in tangible property implies a similar right to an accurate public attribution of who owns what rights. The common law of defamation gives a person some further rights in the accuracy of communications of others regarding oneself.
Trademark, DNS, plagiarism, and defamation are rights of accuracy in labeling, attribution, and other descriptions related to a person. There are some natural rights to demand of another person's communications that they accurately label and attribute objects and content related to oneself in certain ways, such as ownership or origination.
It's harder, though, to argue that copyright and patent have natural rights analogs. One has to go from a right that a content or idea (as well as property and self) be properly attributed to a person, to imputing to that person a right to exclude others from communications of that content (copyright) or use of that idea (patent), despite that content or idea being instantiated in somebody else's personal property.
The predecessors of copyright were the rights of lords and bishops to control speech and writing within their domain -- a dubious origin given our First Amendment ideals. Copyright still conflicts with free expression. P2P networks originated as proposals for networks that it would be impossible for repressive governments to censor. It turns out, though, that censorship-free networks are also copyright-free networks. Copyright and censorship both rely on having “gatekeepers” who the government can coerce in order to control content. The state of nature on the Internet is copyright-free as well as censorship-free.
In summary, it's much harder to justify as natural law copyrights and patents than legal areas like trademark and defamation that involve the accuracy rather than ownership of information.