I think deficiencies on a vegetarian or vegan diet have more to do with poor eating than with eschewing meat, eggs, or dairy. (After all, omnivores who eat poorly develop deficiencies, too, especially of B12 as sparrowrose said.) I track my nutrient intake periodically and my macronutrient intake every day and often get 70+ grams of protein, much more fiber than called or (50 or so grams instead of 20), plenty of vitamin A from raw and cooked veggies and fruits, plenty of magnesium from whole grains, fruit, and vegetables, B12 from supplements, iron from nearly everything (it's better absorbed with the addition of something with vitamin C, like raw fruits and vegetables [cooking degrades vitamin C]), and calcium from fortified milks, nuts, vegetables, grains, etc.
With that said, it is important to be watchful over your diet to eat healthy, whole foods, but I don't think veganism or vegetarianism is so apt to cause deficiencies per se. :)