It all depends on what you mean by "off the grid".
If you're truly "off the grid" you don't own the land, you're not paying taxes, and you have no social security number. If all these things are true, you really don't exist within the government's eyes.
And yes, there are people who live off the grid. How many? Who knows?
So, is it illegal?
Technically "yes". Everyone has to have ID and pay taxes. However, as you have no postal address, no income, no possessions, and no way to be tracked - the government has to find you first. If they have no evidence that you exist, they're probably not looking for you. If you do all your transactions with cash, there's no reason why they should be looking for you. Keep your nose clean from things like murder, armed robbery, and other major crimes and you'll be a ghost in the system.
When you're truly "off the grid" you're pretty much invisible to the system.