Depending on historical records 18 to 23 schools are now extinct. 3 traditions are surviving from these schools, Theravada calls itself the original teachings of Buddha, Mahayana also says it has the original teachings of Buddha along with sunyata and bodhisattva views in the Prajnaparamita, which has many schools including Vajrayana which matured and flourished around the lands of Tibet and surrounding countries.

Schools / Lineages
Theravada - Teachings of the Elders
Mahayana - The Great Vehicle
Vajrayana - The Thunderbolt Vehicle
The Chinese Schools
Japanese Buddhist Schools
A Comparative Study of the Schools