Vegetarianism is only a standard practice in Mahayana Buddhism, and typically only for monastics. Laity practice vegetarianism only on Observance Days (Uposatha), of which today is and yesterday was. If you already happen to be vegetarian, you're expected to fast. Mahayana vegetarianism can be found discussed within the Lankavatara Sutra. I think it's in the last chapter.

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Interview with monk regarding the lay practice of not eating meat on Lunar Observance Days:

"Fasting in the lay community in Asia is typified by the Chinese word 'zhai' or 'zai', which means at the same time 'vegetarian' as well as 'fasting.' The point is that removing the meat from one's diet, twice a month on the new or full moon days, or six times a month, or more often, is often considered already a kind of fasting. The principle holds that removing indulgences from the diet, in this case, nutrients that are luxuries eaten to satisfy the desire for flavor, is already a form of fasting, and brings merit to the one who fasts."

Anecdotal: I'm Vietnamese and our practices are virtually identical to Chinese Buddhism. My family practices vegetarianism on the new and full moons, plus the days preceding it. This is easy to track, as it is the 1st, 14th, 15th, and last day of every lunar month. I believe, but cannot confirm, that this is common practice, so I think the wording of "on the new and full moon days" is speaking generally. I think I can take as a point that today--September 16th--is a full moon, but the Mid-Autumn Festival started yesterday.

Excerpt of the Lankavatara Sutra:

The Buddha told Mahamati: "Meat eating has countless offences. All Bodhisattvas should cultivate their great mercy and compassion so that they should not eat meat. Now I am telling you in brief the merits of not eating meat, and the offences of meat eating, please listen attentively."

"Mahamati, I see that from the beginningless time, because of the habit of meat eating and the greed for flavors of meats, living beings kill and hurt each others in never ending cycles, thus they are apart from sages and suffering from births and deaths."

"Those who renounce the flavor of meat can taste the flavors of the true Dharmas, truthfully practice the Bhumi(stage)s of Bodhisattva, and attain Anuttara-Samyak-Sambodhi quickly. They can then make all living beings enter the resting-place of Sravaka(voice-hearer) and pratyeka-buddha(self-enlightened one), and after that make them enter the stage of Tathagata."

"Mahamati, these benefits are based on the merciful heart. People who eat meat are destroying the great merciful seed of their own, then how could they get these great benefits?"

"Mahamati, I see that living beings are in the transmigration of the six paths, being together in births and deaths, they give birth to and foster each others, and cyclically become fathers, mothers, brothers and sisters of each others; They may be men or women, may be the direct line of descent, may be cousins, affinities, uncles, aunts, sons, daughters, grandsons, and other various relatives of each others; They may also be born in other paths(of animal, ghost, god, and so on.), whether virtuous or evil, they frequently become the relatives of each others. Because of these relationships, I see that all meats eaten by living beings are of their own relatives. Due to the greed for flavors of meats, the living beings circularly eat each others, then they always have the thoughts of hurting each others. Their painful karmas are always increasing, so they are wandering in cycles of births and deaths and unable to escape."

Source

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The other sects of Buddhism follow the triple-clean rule for eating meat: meat is to be refrained from when it is known or suspected that it hasn't been killed for you explicitly (I forget the third part), and this is really just to avoid generating new karma. Otherwise, meat is fine to accept for food provided it wasn't killed for you and has already been prepared. I forget the name of the sutta this comes from, will look it up when I get back into the office.

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The Theravadin policy on meat is found in the Jivaka Sutta (Majjhima Nikaya 55) :

Jivaka, I say that on three instances meat should not be partaken, when (1) seen, (2) heard, or when (3) there is suspicion. I say, that on these three instances meat should not be partaken. I say, that meat could be partaken on three instances, when not seen, not heard, and not when there is suspicion about it.

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Tibetans typically follow the latter rules because edible vegetation is hard to come by in the Tibet, and some Tantric practices include the consumption of meat.

I know very little about Greco-Buddhism, other than its association to Gandhari Buddhism. As such, they probably either observed Mahasanghika or Sarvastivadin rules (the two major Vinaya lineages in Central Asia before they went extinct). I haven't gone through enough of Vasubandhu's Abhidharmakosabhasyam yet to know their position on the consumption of meat, however, if it's recorded anywhere, it's probably in that text somewhere. I'll provide links to this when I get in the office as well.

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I searched the texts for any mention of meat policy in Vasubandhu's work, but it doesn't seem to be there. In the footnotes of Volume II, there is some brief mentions, but nothing substantial and certainly nothing specific to either the Mahasamghika or Sarvastivadin Vinayas (neither of which are translated into English AFAIK).

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