SWL in a car in the U.S. may be an indulgence for those who are enthusiasts and there are some choices out there.
KARADIO offered the 80-C shortwave car radio in the early '50's. There are probably none around now and it was back when cars were 6 volts. A modern receiver would be a much better choice. http://www.radiomuseum.org/r/eckstein_internationalthe_80c.html
I haven't seen a used Philips DC-777 mentioned yet and would put that out there as a possibility: http://www.universal-radio.com/catalog/portable/DC777.html
I think that it got good reviews in Monitoring Times back in the '90's.
Mobile SWL hardware outside the U.S. is probably more useful than it is here, but there is always something to listen to.
I leave for work before dawn and listen to AM-DX on my way in. Local late night programming can lack in many ways. I don't care to listen about flying saucers or political drama call-in shows. There are times you stumble upon something that is actually pleasant and unexpected to listen to.
Sometimes when driving next to telephone poles out in the rural areas, the RFI is worse than the city. Broadband internet noise?
I hardly ever listen to FM and my wife never listens to AM. She had a free 90-day SiriusXM trial with her new Jeep, but I can't see paying a monthly subscription for radio.
I upgraded my car radio to a Chrysler RAK with RDS, so I am contemplating the BST-1 converter mentioned a couple of posts above. RDS will allow you a frequency readout in the display. http://www.wkjeeps.com/wk_radios.htm#RAK