Has there ever been a case of conjoined triplets?

No there has not. However, there has been a case of conjoined pig triplets, according to Ripley's believe it or not. They only lived for several minutes before total organ failure. These piglets have been the only conjoined triplets ever recorded. read more

There have been no live births of conjoined triplets; however, a 2004 study in the American Journal of Obstetrics & Gynecology recorded a one-of-a-kind case of conjoined triplet fetuses. The three fetuses were diagnosed in the womb and removed through an emergency hysterotomy. read more

Case #1 For Conjoined Quadruplets: The article also states that regardless of the immensity low odds, there has been one case of conjoined quadruplets. In Norway, September 5, 1953, two of the four babies were conjoined, but had died at birth. read more