Buddhism, along with Jainism, recognizes that even eating vegetables could contribute to the indirect killing of living beings as animal life is destroyed as farmers plough land. Jainism consequently considers death by starvation as the ultimate practice of non violence, while Buddhism considers extreme self-mortification to be undesirable for attaining enlightenment.
Both Mahayana and Theravada theology generally hold that meat eating in and of itself does not constitute a violation of the Five Precepts which prohibit one from directly harming life. Pali/Sanskrit term for monks and nuns means one who seek alms.
However, when monks and nuns who follow the Theravada feed themselves by alms, they must eat whatever leftover foods which are given to them including meat. Exception to this alms rule is when monks and nuns have seen, heard or known that animal(s) have been specifically killed to feed the alm seeker or guest, in which case, consumption of such meat would be karmically negative. This is also followed by lay Buddhists; and is known as the consumption of the 'triply-clean meat'.
On the other hand, when lay communities specifically purchase meat for consumption of monks and nuns, permissibility of meat eating differ among different Buddhist sects. Theravada Pali Canon records instances of Buddha eating meat which were specifically purchased for Buddha. This act was deliberately performed by the Buddha to demonstrate that if need be, a Buddhist can bend the rules in times of emergency or inconvenience. Obstinately observing vegetarianism or Buddhist rules in times when you cannot, conflicts with Mahayana philosophy because obstinacy or attachment for anything, is considered to be 'stubbornness'  which will become an obstacle to nirvana or enlightenment. However even then, if one undertakes a vow to be a Buddhist vegetarian, one is expected to follow this vow until it is humanly impossible to continue one's vegetarian diet.
Acceptance of authenticity of the Pali Suttas differ within Mahayana sects and Mahayana sutras do not record Buddha eating meat. While no Mahayana sects consider Pali sutras to be inauthentic, Chinese Buddhist sects tend to consider this particular part of writing in Pali suttas to be false. Japanese Buddhist sects generally accept that Buddha ate meat.
Still, both Mahayana and Theravada Buddhists consider that one may practice vegetarianism as part of cultivating Bodhisattvas's paramita. Since Mahayana Buddhists recognise the consumption of meat to be cruel and devoid of compassion, some Mahayana Buddhists are vegetarians. Numbers of Mahayana sutra record Buddha praising the virtue of avoiding meat.
However, Tibetan Buddhism believes that tantric practice makes vegetarianism unnecessary. All Japanese Kamakura sects of Buddhism (Zen, Nichiren, Jodo) have relaxed Mahayana vinaya, and as a consequence, do not practice vegetarianism but rather pescetarianism. Chinese Buddhism and part of Korean Buddhism strictly adhere to vegetarianism.