Intangible personal property. Personal property for sure. Intellectual property would also be personal property. Only real estate and the structures built upon it is defined as real property.
Rather than give a long and possibly boring explanation, I invite you to read a pair of comments from 2 competent lawyers on the subject being discussed: http://www.dnforum.com/f26/help-please-2-thread-272351.html#post1355013 http://www.dnforum.com/f26/help-please-272351-post1355238.html#post1355238
A valuable discussion, Dave, thanks. I did not know: That domains do not necessiarly pass to heirs at death and that domains are not subject to bankruptcy seizure. All in all, domain law is a new field and much of what a domain really "is" is yet to be decided in the courts.
Oh, those 2 comments from John Berryhill and Brett Lewis indicate how domain names have been decided on specific circumstances. But if you're referring to like an all-in-one capacity, I doubt that'll ever happen, given how complex all that is. You might want to read those 2 links I posted earlier if you haven't yet. They can save one from possibly deluding himself into thinking what isn't.