I often found web sites with solid black text on total white to be too overpowering, as do many people and this is why very dark grey is most often used on professionally designed web sites. A more subtle color helps the over all piece look better as well as being easier on the eyes. Now I generally go for a dark grey that still reads as black. Usually something around #333333 give or take a bit. It’s a cleaner look. We are talking about a shade of grey that is still basically perceived as black, but is soft enough that it becomes a part of the art on the page.
I researched the internet to see what others thought and the overwhelming response is a preference to very dark grey as opposed to solid black. This is also true in some print situations as well.
I have also seen sites where the text is way too grey to the point you could hardly read it. This is also a big DO NOT DO. Too many sites go too far with the grey which then makes people question the practice.
I came about the use of shades of grey text earlier in my career when I noticed my websites just seemed too contrasty and the solid black text seemed so out of place with the colors of the page. I realized other designers where using shades of grey or even color, which really made their designs a lot more attractive so I began practicing this myself and my designs began to look way better.
You definitely want enough contrast for readability, but too harsh of a contrast can also be an eye strain so the point is to pull back on the black just enough to hit that sweet spot.