There are so many health benefits that I don't have time to name them all. Google John McDougall, MD, Neal Barnard, and cardiologist Caldwell Esselstyn to get filled in on the many ways it helps. Mainly the freedom from worry about so many of the diseases that plague our society. No need to worry much about gaining weight, unless you keep on eating and drinking sugary stuff(bad idea, anyway).
I like to know that I am not contributing to the cruelty to animals caused by supporting the meat industry -- not directly a health benefit, but a weight off my conscience. I confess I am not a perfect vegan in that I feel a need for fish oil supplements to counter bursitis in my shoulders due to old injuries. Lately I have also been eating a few free-range eggs, as an experiment. (The chicken is going to lay the egg one way or the other, is the way I look at it.) Hardcore vegans insist you can get the Omega-3 fatty acids from green leafy vegetables, but I really haven't put this to the test.
Bottom line is, eating the vegan way is great. I have done so for about the past 3 or 4 years. I'm 63 and work hard/play hard. My body is holding up great, while many of my contemporaries are dying shortly into retirement. Check out Vegsource.com to get the whole picture of the many benefits to society and the environment if more of us went vegan. I believe it's the diet we are built to eat, as do our closest animal relatives, the chimps. Very hard to explain how liberating it is. Try it for a while and you'll see.