I missed the world 6th spot, Hyundai on the list of car producers. Thanks to Chris' noting this, I can add them now. Hyundai as a brand doesn't do much for me, but clearly many disagree going by the brand's success. It managed a solid growth in production for 2012, even increasing worldwide share to 5.4%.
In 2005, 71% of Hyundai's manufacturing was local, but that is now 42.5% as you can see in the chart. Korean numbers only grew 1%, while Russia increased 61%, the Czech Rep 21%, and China 15%. Total production was up 8%.
In the list below, yellow represents Asia, blue America and green Europe.
Data source: OICA