I swear to God the following story is true, and happened to me in about 2002.
I was driving through New Mexico around 2 am or so one night on a remote section of I-40 heading west. I had the cruise control set at about 88 mph and there had been no cars anywhere in sight for some time.
I was traveling in the left lane where the pavement was smoother. Headlights of a car appeared in my rear view mirror. The car was slowly closing on me, so I moved over into the right lane to let them pass.
As the car passed me, I looked over to see who was "out speeding me". The car was a basic 80's four door sedan, white, and I could not see anything inside it. As the car passed, I looked at the license plate to see where "they" were from. The plate was sort of "blurry" as I recall, and I could not tell what state it was.
After the car passed me, it moved over into my lane and then started to slow down. This forced me to break my cruise speed (and really annoyed me). So I moved into the passing lane, and hit the gas. When I had passed the car by 15 feet or so, I checked my side mirror to assure that there was "just enough room" to cut back in front of him.
As I was changing lanes, the lights of this car disappeared. It totally freaked me out, and I immediately let off the gas, looked everywhere behind me, but the car had vanished. I stopped my car, and got out to listen and look more.
It was a moonlight night, flat open desert all around, no sound, no dust, just absolute stillness. There is no logical, physical place that car could have gone, it just disappeared.