If you're into nutrition science, these two papers by D Joe Millward offer an excellent summary of the state of the science surrounding protein requirements.http://journals.cambridge.org/download.php?file=%2FPNS%2FPNS58_02%2FS0029665199000348a.pdf&code=de953b2ff0848a5ee332fec41a70bb64http://ajcn.nutrition.org/content/72/1/112.full.pdf
The summary is this: first, there is some reason to be concerned that vegans could be deficient in the amino acids that are less common in plant foods. (Usually lysine.)
However this problem is easy to overestimate, even in the scientific literature, because it is so difficult to accurately assess AA requirements, other than by lowering AA intake in children until growth is stunted, which is not an ethical study design. (And other animals are not excellent proxies for this information; rats have a different set of required amino acids, for instance, which was the cause of the original soy scare.)
So two types of tests are typically done: One is to take protein-deficient (i.e. starving) children, and feed them a controlled diet, and measure AA intake. However, now we know that the body knows it's in a deficit, and absorbs AA's at a much higher rate when recovering from starvation. This method has vastly overpredicted AA requirements, even for children (who need much more protein than non-pregnant/breastfeeding adults).
The other is to measure AA metabolism through fancy isotope labeling in adults. I don't pretend to understand the mechanism, but basically measure when AA needs are met. However now we know that the body adjusts how much protein to burn for energy (de-novo glucogenesis) before it can be absorbed, based on the amount of protein the person typically eats. So this effectively finds that you require about the amount of protein that you normally eat. This is circular reasoning, and doesn't speak to actual requirements.
The second paper introduces a fancier isotope labeling measurement that somehow accounts for this (hand wave hand wave), which finds a lower requirement, such that typical vegan diets, as well as most of the world's traditional staple starch diets, are fine.
So kids, expecting and breastfeeding moms -- try to eat high-lysine foods a few times a day. (Legumes, and anything vegans eat as meat replacement, it turns out is high lysine -- beans, lentils, tofu, tempeh, seitan, quinoa, hummus, soy milks and yogurts, nuts, and maybe even wheat products.)
Veganhealth.org suggests that adults do this too, although reasonable people could disagree about adult requirements.
I think I've wasted enough time on this for right now. :) (Can you tell this is a topic I care about?)