Based on the definition of vegetarian as a diet which excludes consumption of animal flesh, technically, yes, eggs are vegetarian, since they are not animal flesh (the meat, muscles or tissue of an animal). Many vegetarians include eggs in their diet, while still abstaining from eating chicken, cows, pigs, fish and all animals. According to terminology, you're an "ovo-vegetarian," that is, a vegetarian who eats eggs. Note that while eggs are vegetarian, they are certainly, under no circumstances, considered vegan.