Originally Posted by http://en.wikipedia.org/wiki/Polycephaly
Polycephaly is a condition of having more than one head. The term is derived from the stems poly- meaning 'many' and kephal- meaning "head", and encompasses bicephaly and dicephaly (both referring to two-headedness). A variation is an animal born with two faces on a single head, a condition known as diprosopus.
Dicephalic conjoined twins (dicephalus dipus):
In 1990, Abigail and Brittany Hensel were born in Minnesota, United States
In 2000, Ayse and Sema were born in Kahramanmaraş, Turkey
In 2003, June 13, twin girls named Huda, and Manal Abdel Nasser Mohammed Mahmoud, were delivered Caesarean section in a hospital in Asyut, Egypt
In 2003, Sohna and Mohna were born in India
In 2006, Syafitri was born in Indonesia
In 2007, Mary Grace and Mary Divine Asis were born in the Philippines having only one heart. 
In 2008, August 25, a baby boy named Kiron was born with two heads in south-western Bangladesh.  Kiron had been born from one embryo but a serious development anomaly had been present resulting in the double heads. The baby was described by the gynaecologist present at the birth as having "one stomach and he is eating normally with his two mouths. He has one genital organ and a full set of limbs".  However the clinic initially had been unable to determine whether he had one or two sets of vital organs.  The mother and baby had been taken to a hospital in Jessore, but the hospital staff had attempted to refer him to a more resourceful hospital in Dhaka in an attempt to save it. However the family lacked the money to take him there despite donations.  Although the baby had initially been healthy and was eating well, on August 26 the baby encountered breathing difficulties and a fever and subsequently died two days later on August 28.
Craniopagus parasiticus - parasitic twin head with an undeveloped (or underdeveloped) body attached to the head of a developed twin:
In 2003, Rebeca Martinez was born in the Dominican Republic with an extra head but died 7 hours after surgery at the age of 8 weeks.
In 2004, Egyptian Naglaa Mohamed gave birth to Manar Maged who had the head and undeveloped torso of another child attached. In 2005, the second head was removed, and later that year Naglaa appeared on the Oprah Winfrey show with her surviving child. Manar died from a brain infection in 2006.
Maria and Consolata Mwakikoti from Tanzania (b. 1999)
Luz and Milagros Romero-Saucedo of Argentina (b. 1999) may or may not be of the dicephalus type.
Carmen and Lupita Andrade-Solis (b. 2000), originally from Mexico, currently resident in Connecticut, United States
In 2008, a female child named Lali was born to Vinod and Sushma Singh of the Gautam Buddha Nagar district of Uttar Pradesh in India.  The family has refused special medical care, and recent reports state that the case is not one of polycephaly, but a condition called craniofacial duplication, a rare congenital disorder. 
Two-faced kitten, Lausanne
There have been numerous reports of two-faced cats; most die soon after birth. Reports of two-headed kittens are common, relative to other animals, because of their status as household pets. Recent two-headed kittens include:
On 2008-11-19, A two-faced kitten was born in Perth, Australia. 
On 2006-07-12, Tiger, a two-faced kitten was born in Grove City, Ohio.
On 2005-06-12, Gemini, a two-faced kitten was born in Glide, Oregon.
On 2005-03-08, Deuce, a two-faced kitten, was born in Lake City, Florida, and was euthanized shortly thereafter, having come down with pneumonia.
On 2000-06-07, Image, a two-faced kitten, was born on and died later that year in Philadelphia, Pennsylvania.
Polycephalic cats in museums include:
The Museum of Lausanne in Lausanne, Switzerland, preserves a two-headed kitten (pictured).
The Laing Museum in the small town of Newburgh, Fife, Scotland, preserves the stuffed body of a two-headed kitten born in the 19th century on Mugdrum Island.
The Georgia State Capitol in Atlanta, Georgia, has a full body taxidermy of a two-faced kitten.
Ripley's Believe It or Not! Museum on Clifton Hill in Niagara Falls, Ontario (Canada) has a full-body taxidermy of a two-faced kitten.
Two-headed calf, Lausanne
A head mount of a two-headed calf is on display in the Museum at the Georgia State Capitol Building in Atlanta, Georgia.
A two-faced calf is preserved at the Douglas County Museum in Waterville, Washington. The calf lived for ten days after birth.
The Ripley's Believe It or Not! museum in Gatlinburg, Tennessee, has full body taxidermy of a two-headed calf.
The Dalton Gang Museum, located in Meade, Kansas, also displays a full body taxidermy of a two-headed calf.
A two-headed calf mount can be found at the Old State House in Hartford, CT
A full taxidermy of a two headed calf can be found in Melton Mowbray museum, Leicestershire, Uk
A full taxidermy of a two headed calf can be found in the Museum of Marxell (in the Northern Black Forest in Germany). The calf was born by a local cow and died shortly after birth by natural causes.
Two-headed piglet; Old State House, Hartford, CT
A two-headed piglet can be found at the Old State House in Hartford, CT
In 1998, Rudy, a two-headed pig was born in Iowa.
Goats and sheep
Two-faced lamb, Lausanne
In 2006, a two-headed lamb was born in Shandong, China.
The Ripley's Believe It Or Not! museum in Gatlinburg, Tennessee, has a mount.
A two-headed black rat snake with separate throats and stomachs survived for 20 years.
There are several preserved two-headed snakes on display in the Museum at the Georgia State Capitol Building in Atlanta.
Two-headed turtles and tortoises are rare but not unknown. Recent discoveries include:
In 1999, a three-headed turtle was discovered in Tainan, Taiwan, by a villager named Lin Chi-fa.
In 2003, a two-headed angulate tortoise was discovered in South Africa, with the only other known case in the region reported in the early 1980s.
In 2004, Solomon and Sheba, a two-headed Mediterranean spur-thighed tortoise was born in Dorchester, England.
In 2005, a two-headed Olive Ridley sea turtle was found in Costa Rica by the World Wildlife Fund.
In 2005, a baby turtle of unknown species was also reported in Havana, Cuba, in 2005.
In 2006, a two-headed, six-limbed soft-shell turtle in Singapore named "Double Happiness" was also featured on a local television program, and again on another program in late 2006.
As of 2006, a living two-headed Greek Tortoise named Janus is being displayed in the Museum of Natural History of Geneva.
There is a full body mount of a crocodile with two heads located at the Georgia State Capitol on the top level.
As of 2007, there is a fully preserved Common Snapping Turtle named Emily with two heads at the Science Museum of Minnesota.
Currently there is a two-headed Florida Redbelly Turtle named Gege living at the Homosassa Springs Wildlife State Park.
"..not all those who wander are lost.." j.r.r. tolkien
Specification of the anterior dorsal/neural axis in vertebrates is now very well understood. There are lots of famous experiments in developmental biology that result in embryos with multiple heads. One of the genes that has been identified as playing an important role in this process is aptly named Cerberus (after the mythological three-headed-dog). Mis-expression of this gene during embryonic development causes the development of extra heads.