What teachings do all schools of Buddhism share? Among the many schools and traditions, what core teachings are shared by all Buddhists?
There is an existent reference to the similarities between Theravāda &amp; Mahāyāna which I will cite:
(I think it also applies to Vajrayāna although I may be wrong in this regard.)


  
  Whatever our sects, denominations or systems, as Buddhists we all accept the 
  Buddha as our Master who gave us the Teaching. 
  We all take refuge in the Triple Jewel: the Buddha, our Teacher; the Dhamma, his 
  teaching; and the Sangha, the Community of holy ones. In other words, we take 
  refuge in the Teacher, the Teaching and the Taught. 
  Whether Theravada or Mahayana, we do not believe that this world is created and 
  ruled by a god at his will. 
  Following the example of the Buddha, our Teacher, who is embodiment of Great 
  Compassion and Great Wisdom, we consider that 
  the purpose of life is to develop compassion for all living beings without 
  discrimination and to work for their good, happiness and peace; and to develop 
  wisdom leading to the realization of Ultimate Truth. 
  We accept the Four Noble Truths taught by the Buddha, namely, Dukkha, the fact 
  that our existence in this world is in predicament, is impermanent, imperfect, 
  unsatisfactory, full of conflict; Samudaya, the fact that this state of affairs is due 
  to our egoistic selfishness based on the false idea of self; Nirodha, the fact that 
  there is definitely the possibility of deliverance, liberation, freedom from this 
  predicament by the total eradication of the egoistic selfishness; and Magga, the 
  fact that this liberation can be achieved through the Middle Path which is eight-
  fold, leading to the perfection of ethical conduct (sila), mental discipline 
  (samadhi) and wisdom (pañña).
  We accept the universal law of cause and effect taught in the Paticcasamuppada 
  (Skt. pratityasamutpada; Conditioned Genesis or Dependent Origination), and 
  accordingly we accept that everything is relative, interdependent and interrelated 
  and nothing is absolute, permanent and everlasting in this universe. 
  We understand, according to the teaching of the Buddha, that all conditioned 
  things (samkhara) are impermanent (anicca) and imperfect and unsatisfactory 
  (dukkha), and all conditioned and unconditioned things (dhamma) are without self (anatta). 
  We accept the Thirty-seven Qualities conducive to Enlightenment 
  (bodhipakkhiyadhamma) as different aspects of the Path taught by the Buddha 
  leading to Enlightenment, namely, 
  
  Four Forms of Presence of Mindfulness (Pali: satipatthana; Skt. smrtyupasthana); 
  Four Right Efforts (Pali. sammappadhana; Skt. samyakpradhana); 
  Four Bases of Supernatural Powers (Pali. iddhipada; Skt. rddhipada); 
  Five Faculties (indriya: Pali. saddha, viriya, sati, samadhi, panna; Skt. sraddha, virya, smrti, samadhi, prajna); 
  Five Powers (bala, same five qualities as above);
  Seven Factors of Enlightenment (Pali. bojjhanga; Skt. bobhyanga); 
  Eight-fold Noble Path (Pali. ariyamagga; Skt. aryamarga).
  
  There are three ways of attaining Bodhi or Enlightenment according to the ability 
  and capacity of each individual: namely, as a Sravaka (disciple), as a 
  Pratyekabuddha (Individual Buddha) and as a Samyaksambuddha (Perfectly and 
  Fully Enlightened Buddha). We accept if as the highest, noblest and most heroic 
  to follow the career of a Boddhisattva and to become a Samyksambuddha in order 
  to save others. But these three states are on the same Path, not on different paths. 
  In fact, the Sandhinirmocana-sutra, a well-known important Mahayana sutra, 
  clearly and emphatically says that those who follow the line of Sravaka-yana 
  (Vehicle of Disciples) or the line of Pratyekabuddha-yana (Vehicle of Individual 
  Buddhas) or the line of Tathagatas (Mahayana) attain the supreme Nirvana by the 
  same Path, and that for all of them there is only one Path of Purification 
  (visuddhi-marga) and only one Purification (visuddhi) and no second one, and 
  that they are not different paths and different purifications, and that Sravakayana 
  and Mahayana constitute One Vehicle One Yana (eka-yana) and not distinct and 
  different vehicles or yanas.
  We admit that in different countries there are differences with regard to the ways 
  of life of Buddhist monks, popular Buddhist beliefs and practices, rites and 
  rituals, ceremonies, customs and habits. These external forms and expressions 
  should not be confused with the essential teachings of the Buddha.  
  
  
  -One Vehicle for Peace by Ven. Walpola Sri Rahula, (December 1–7, 1981)