The American Dietetic Association officially endorses vegetarianism, and books by prominent doctors promote low-fat vegan or mostly-vegan diets (e.g., . Dean Ornish's Program for Reversing Heart Disease). Vegetarianism dates back to a time before recorded history.
Many anthropologists believe that most early humans ate primarily plant foods, being more gatherers than hunters.
Certainly humans started eating meat at some point before recorded history, but only because unlike animals, humans are capable of that kind of experimentation.
For anatomically and physiologically plant-only diets in non-human animals, see herbivore. Other motivations for vegetarianism are health-related, political, environmental, cultural, aesthetic, economic, or personal preference.
There are variations of the diet as well: an ovo-lacto vegetarian diet includes both eggs and dairy products, an ovo-vegetarian diet includes eggs but not dairy products, and a lacto-vegetarian diet includes dairy products but not eggs.
(See articles by David Popovich and Derek Wall.) This view is supported by the fact that the human digestive system resembles that of other plant-eaters rather than that of carnivores.
(Forget about "canine" teeth -- other herbivores have them too.