Yes, there is a discipline called natural apnea or natural weight. It is practiced (besides others) for example in Greece, during the
Kalymnos festival. The divers do not use any equipment (no mask/goggles, fins, weight) in this discipline.
The most known natural freediver is probably
Danai Varveri (Δανάης Βαρβέρη), Greek female freediver who was pictured also in the movie The
Freediver of Alki David, and who did a 40m dive in 1999 and I believe another even deeper in 2004. The fictive Danai Varveri in The Freediver movie dies during a competition, but AFAIK, the real Danai lives in Greece and is still involved in diving activities.
More information about Danai is available for example in WikiPedia:
http://en.wikipedia.org/wiki/Danai_Varveri
or at Apnea.nl:
http://www.apnea.nl/UK-GeschDanai.htm
There is one video of the real Danai in my collection:
http://apnea.truxoft.com/#Varveri
and also a trailer from The Freediver movie:
http://apnea.truxoft.com/#movies
Some natural apnea records are listed for example
here, but it is rather outdated.
