If my car was rear-ended and the at-fault driver’s insurer wants to total my vehicle but isn’t offering very much for it, what can I do?

To the extent that the other driver was 100% at fault, then he or his insurance company owe you either the repair cost or the fair market value of your vehicle if the repairs cost more than the vehicle's fair market value.  While "fair market value" is somewhat imprecise, it usually is established by a book value (Kelly Blue Book, NAPA Guide, etc.) or perhaps by comparable sales in your area, etc.  It also may be somewhat negotiable, particularly if there is something special about your vehicle that they are unaware of (new tires; recent substantial repairs; options; etc.).  All that said, it is worth what it is worth and you may well not be able to buy a replacement vehicle that is comparable for the money they give you.  You might also make a deal with them for you to buy back your vehicle for salvage value or otherwise keep it if you want.  Understand that any necessary repairs would then by on you (but you would have whatever they otherwise paid you to help with those repairs) and your vehicle would presumably have a branded, salvage title thereafter so it's resale value would drop drastically.  While you might (or might not) be able to get liability insurance on it thereafter, it is unlikely that an insurance company would give you collision or comprehensive insurance if you have a salvage title.  At a minimum, if that is important to you, you should check out such availability with your insurance company before go forth with such a deal.  Good luck.