Yes, if you are not a body builder or looking to gain muscle, you most likely get plenty of protein if you eat healthy, even without any animal products.
I believe that the emphasis on protein and calcium (from animals) stems from the amount of power the meat and dairy industries hold. Many doctors advise against consuming so much from animals and many also fervently disagree with our food pyramid.
Has anyone ever wondered why the US has such a high rate of osteoporosis, especially in women, yet we consume more calcium from milk than most places on the planet?
I am not saying protein is not important, but it should not be emphasized as much as it is, especially protein from animals. If anything, fiber and vitamin c should be, do to the gross lack of consumption of the two here in the US. Also, the idea that protein from natural sources is not "complete" is false.
With that said, if you want to build more muscle, you need more protein. While you can certainly get this by increasing the amount of clean foods you eat with high amounts of protein, such as broccoli and beans, it is often easier to consume a protein powder for several reasons.
I have recently, as in two days ago, decided to buy some whey protein powder. I have been using hemp protein (all natural, from hemp) for the past week, but it just tastes terrible, like grass. I have chosen two of the least refined brands, jay robbs and any whey. Yes, whey is from cow's milk, but this is one of the few animal products I consume per day (1 egg, 1 slice of no-antibiotic roast turkey (sometimes), and tuna in my salad, a great protein boost). I am very happy with my diet and have no problem using whey protein (I do have to cut out my ice cream, though

).
If you want to do some research of your own, a good place to start is the China Project. Another is Dr. Fhurman's Eat To Live, which is basically just a book of research that has been done over the years regarding the effects of foods on the human body.
Wow, this turned out rather long. So, long story short, if you don't want to build muscle, don't concern yourself with protein, just make sure you eat ALOT of fruits, veggies, legumes, and whole grains and make sure you get adequate amounts of vitamin B-12. If you do, just figure out what works best for you, be it more beans or a protein powder. Good luck!!!