+ They bear appropriate passports issued by competent authorities of Japan or the Republic of Korea and still valid for up to 3 months from the date of their entry;
+ They have return tickets or tickets to travel to another country;
+ They are not in the list of persons not permitted to enter Vietnam.
(Decision No. 09/2004/QĐ-BNG dated June 30, 2004 by the Minister of Foreign Affairs promulgating Temporary Regulations on exemption of visa for citizens of Japan and citizens of the Republic of Korea.)
Decision No. 09/2004/QĐ-BNG still valid till now, however, according to updated LAW Number: 47/2014/QH13 dated June 16, 2014, Article 20. Conditions for entry, saying that : "A foreigner who is eligible for visa exemption upon entry under an unilateral visa exemption scheme must have a passport that remains valid for at least 6 months, and the interval between the entry date and the previous exit date must be at least 30 days". Therefore, Japan & Korea Republic passport holders can enter Vietnam without entrance visa but the entry date must be at least 30 days from the previous exit as unilateral visa-exempted person. Otherwise that person is required to have appropriate visa to enter Vietnam.
In other words, you must exit Vietnam for 30 days then eligible to re-enter Vietnam for visa-free-entrance or apply for a visa if your entry date not enough for 30 days from your previous exit date.
Please see Decision No. 09/2004/QĐ-BNG dated June 30, 2004 in Vietnamese version here & Updated law On foreigners’ entry into, exit from, transit through and residence in Vietnam
Updated : According to Resolution No. 99/NQ-CP dated on December 29, 2014, you don't need to show return tickets or tickets to travel to another country.