Do people of today have any additional inalienable rights?
In some ways, the idea of "inalienable rights" was not an invention of any particular time period but one that the framers of the constitution (as well as those who penned the Magna Carta and other similar documents) tried to acknowledge in their construction of a government.
There are certainly no large conceptual rights that have been invented since that particular phrase was made popular, some might argue that some of the changes in technology and elsewhere have actually impeded on the "inalienable" rights of many.
And there are still innumerable places around the world where people's "inalienable" rights are violated on a regular basis, even in places where they are enshrined in documents like the constitution, etc.
Despite what governments may promulgate, Rights, by definition, are inalienable. They are not able to be taken from an individual, or even surrendered by that individual; you possess them forever by virtue of birth. The exercise of Rights, or Freedom, may be lawfully restricted; my Rights end where yours begin. Where that line is, is the only reasons governments should be instituted among people.
There isn't (and will never be) a complete "list" of Rights; anyone, at any time, may do anything he or she desires, as long as such exercise of Rights does not infringe upon another's. That is the whole of the law.