There are two major Vegetarian positions on the egg. One is to eat eggs and the other is not to eat any eggs. The choices are any egg, free range eggs and no eggs what so ever.
Lets look into this deeper, vegans do not want to eat any eggs. The reasons are the hens are battery hens, the beaks are removed, the chicken is forced to lay eggs until they have no calcium left in their bodies and then they are slaughtered. Also, the vegans disapprove of free range birds. The disapprove for the fact that they say the bird is still limited to an hen houses and are not allowed to go outside. A side note from this is that the free range eggs are are also fertile eggs and the male chicks will be grow into chickens that will still be slaughtered.
The less hard core vegetarian will eat eggs no problem. They are sometimes called a ovo-vegetarian. These vegetarians think of veganism as to much of an limit on there options, since eggs are such a good replacement for the protein from meat. It is such a good nutritional alternative to meat. Most of the vegetarians will only have free range eggs, just because of the ethical treatment of the hens.
Some of the other lesser known reasons that vegetarians don't eat eggs is to them the egg has to much cholesterol in them, so its not good for their health. Other vegans believe that the institution animal farming contributes to the environmental being degraded.
So do you side on the nutritionally or the ethically side of to egg or not to egg, make your choice to determine where you stand.