It depends what you mean. If you mean "Are there people living today who claim to be Cathars ?", then the answer is Yes. If you mean "Are there people who live like Cathars, and believe what the Cathars believed ?", then the answer is also Yes.
But neither of these answers tells the whole story. For example, quite a few of the people calling themselves Cathars will tell you that they are reincarnated Cathar Parfaits. But a central Cathar belief was that on their deaths Parfaits were released from the cycle of rebirth. Which means that either these modern Cathars hold to a belief system that they know to be wrong, or that they are impostors who have not troubled to do their homework.
A more interesting question is whether any Cathars living today can claim a continuous chain of succession from the Parfaits of the thirteenth century. The reason that this is significant is that the Cathars themselves claimed a continual chain of descent, each Parfait having joined the inner circle of the Elect by being given the Consolamentum by an existing Parfait. There therefore existed a continuous chain of succession from any Parfait all the way back to the original biblical Pentecost. (If this looks suspiciously like the doctrine of Apostolic Succession claimed by Catholic and other mainstream bishops, it is worth bearing in mind that the mainstream Church is known to have copied the idea from a Gnostic sect in the fourth century, and then fabricated lines of apostolic succession for the missing centuries).
After the depredations of the Inquisition in the fourteenth century, the chain of succession was restored in the Languedoc by two brothers who travelled to Piedmont to receive the Consolamentum from a Parfait there. But this line was apparently exterminated with the burning of Guilhem Belibaste in 1321. The Italian line was exterminated by the Roman Church soon after, and in the fifteenth century the Balkan line was suppressed, or absorbed, by Islam, which shares the characteristically Gnostic belief that it was a divine phantom, not a man, who was crucified when the authorities thought they were executing Jesus (c/f Koran 4:157: "they slew him not nor crucified him, but it appeared so unto them").
Did a secret succession survive from any of these traditions, or from any of the more remote Eastern ones? Perhaps. No one seems to know for sure. But even if not, all of their principal beliefs are to be found in one or another Christian sect. Even the idea that the Roman Catholic Church is mistakenly worshipping the Evil God is still current (Jehovah's Witnesses for example believe this). Also, perhaps significantly, you never hear anyone talking about God in the Languedoc, always specifically the Good God.
Click on the following internal link for more information
on Cathar
ideas and practices still current in modern mainstream Christian
Churches 
Click on the following internal link for more information
on Cathar
ideas and practices still current in Churches other than
Roman Catholic Churches 
Click on the following internal link for more information
on Cathar
ideas and practices now current in the Roman Catholic Church

Click on the following external links to go to websites run by modern Cathar, Gnostic and Dualist Churches
- A network of organisations in the French Gnostic
Tradition
http://www.gnostique.net
- L'Eglise du Plérôme. (Ecclesia Pleromatis). A Church of
Christian Gnosis in the French Gnostic Tradition.
www.plerome.org

-
The North American Fellowship of Cathars (linked with movements in France, Bulgaria,
Bosnia and the Ukraine).
www.cathari.org





