The original Vedic system is actually quite different from contemporary Hinduism. Both the old and the new, however, converge harmoniously in regard to vegetarianism. Here are some quotes from the Vedas:

One who partakes of human flesh, the flesh of a horse or of another animal, and deprives others of milk by slaughtering cows, O King, if such a fiend does not desist by other means, then you should not hesitate to cut off his head." (Rig Veda, 10.87.16)

"You must not use your God-given body for killing God’s creatures, whether they are human, animal or whatever." (Yajur Veda, 12.32)

"One should be considered dear, even by the animal kingdom." (Atharva Veda, 17.1.4)

"Those noble souls who practice meditation and other yogic ways, who are ever careful about all beings, who protect all animals, are the ones who are actually serious about spiritual practices." (Atharva Veda, 19.48.5)

"By not killing any living being, one becomes fit for salvation." (Manusmriti, 6.60)

"The purchaser of flesh performs himsa (violence) by his wealth; he who eats flesh does so by enjoying its taste; the killer does himsa by actually tying and killing the animal. Thus, there are three forms of killing. He who brings flesh or sends for it, he who cuts of the limbs of an animal, and he who purchases, sells, or cooks flesh and eats it—all of these are to be considered meat-eaters." (Mahabharata, Anu. 115:40)

"Those who are ignorant of real dharma and, though wicked and haughty, account themselves virtuous, kill animals without any feeling of remorse or fear of punishment. Further, in their next lives, such sinful persons will be eaten by the same creatures they have killed in this world." (Srimad Bhagavatam, 11.5.14)