Yes Vegatrians can eat eggs. Vegans can't.

It realy depends on the vegetarian - some people self classify.
Technically speaking (apart from the obvious meat and fish)
Vegans - cant eat eggs, dairy, other animal biproducts and some other restrictions
Vegartarians - cant eat eggs, dairy but no other restrictions
Lacto vegetarians - can eat dairy products but not eggs
Ovo-vegetarians - can eat eggs but not dairy
Lacto-ovo-vegetarians - can eat both eggs and dairy.

A lot of it depends on definition - doesn't realy depend on what termininology you use but more about what you eat and don't eat.