If you want to take any of your vehicles off your property, you need to be properly licensed to operate them (and it's hard to even own one without a license, even if you only want to drive 'em around your back yard). Licensing involves both a written safety test and a practical exam, and larger or odder vehicle types require their own separate licenses. There are a very few classes of vehicle that don't require operator licenses, and they're either muscle-powered or very restricted in where they can ever be operated. Your operator license must have your photo and valid home address on it, and can be taken away for any number of irresponsible actions. You can be fined or even (in extreme cases) jailed for operating a vehicle without a valid license, and that includes operation of vehicles not covered by your existing valid licenses.
Every sale of a vehicle must be accompanied by an official transfer of ownership title, so the government knows who sold the vehicle and who bought it. Even if you make your own vehicle from scratch, you need to establish a clear title for it, no matter how much hassle it might cause you (i.e. "One Piece At A Time" by Johnny Cash). Manufacturers of vehicles are under a great number of regulations for safety, and every piece that goes into every vehicle is often tracked quite carefully. The VIN may be the most obvious identification number on a vehicle (and they all must have one, even home-made ones), but most vehicles carry numerous identifying marks and numbers throughout.
You can go online and see the complete history of a used vehicle, and the government makes its records freely available for this purpose.
Here's the punchline: if guns were regulated like cars, people would be freaking the HELL out. And if cars were regulated like guns, I'd be afraid to step out of the house (and would insist on living several stories up).