Out of necessity I've been doing some checking here lately, hence starting this thread. Below 26k GVW it is a state by state requirement. The link crenwelge gave earlier in the thread shows the states that require a state specific DOT number. SC is on the list, lucky for you VA is not. Now what I've gathered is that, in SC at least, any truck over 10K GCVW must have a DOT number if it is engaged in any activity that is "furtherance of a buisness". This is Intrastate (within the borders of SC)commerce only. There is a whole different set of rules for Interstate (crossing state lines) commerce. These are Federally mandated and I believe are consistant from state to state.
I also belive that over 10k GCVW requires at least a health card, in SC. Thankfully, having farm tags on my '52, and our other meduim duty trucks gets us out of having to have a health card and CDL's on our International (33-36k GVW) dumps and spreaders. Note that "C" in GCVW. That is a truck and trailer that grosses over 10K lbs. So a half ton pulling a skid steer loader would qualify.
A truck used for your personal or recreational uses does not have to have DOT number, at least here in SC, but you do have to have a CDL if over 26K GVW, think big motor home. Hope this clears up more than it muddies up. Again, all this applies to SC only. Other states I know have different laws that are as equally confusing.