Virginia personal property tax
The only exception (that I know of - there might also be a veterans exemption, for example) is antique cars with antique plates (over 25 years old and not used for commuting). Still needs insurance to drive on roads. Really old cars with little value are not charged personal property taxes either.
Each county/incorporated city has their own tax rate. All taxes use 100% assessed value which is determined by the "Clean Trade-in Value" established by NADA as fair market value.
Due to skyrocketing used car values, some people were paying hundreds more than they did the previous year. Our county (with rates on the high end $4.28/$100 value) dropped their rates (to $3.42/$100) but I still paid over $1700 this year for a 2020 MY, valued ~$9000 more than the purchase price in 2020. A tax relief credit imposes a lower rate for the first x amt of value.
Least expensive rate I found when checking around online was for WISE county, $1.65 for each $100 of value. Some localities just rejoiced at the windfall. Our more expensive county at least adjusted the rate downward. Personal property charges are mandated by the state and the rate by the locality.