There are a number of posts on this issue. For me the only thing that works consistently in the car is using a 2A charger I bought off Amazon connected to the phone using the white USB cable that comes with the 110 volt Samsung wall charger. It's the cable that seems to be the issue. I can also connect that cable to the USB port of my car and it will charge, but I haven't done that enough to say it's consistent.
For other car chargers, or other cables connected to either that 2A charger or my car's USB port, I get inconsistent results if they work at all. For that Samsung USB 110 volt wall unit, it works with most, but not all, USB cables.
Here's one of the other threads:
http://androidforums.com/samsung-galaxy-s4/790898-gs4-charging-issue.html
Edit: BTW, with that 2A charger and the white USB cable, it seems to charge much faster than it used to--particularly with the screen on.