Update 19.4.
Railway Transportation
JR Kyushu:
Kyushu Shinkansen – All lines are closed.
Kagoshima Line – Closed between Kumamoto and Yatsushiro.
Hohi Line – Closed between Kumamoto and Bungo Taketa.
(New) Planned to resume service between Kumamoto and Higo-Ozu today. (Update) Resume between Kumamoto and Higo-Ozu has been restarted.
Misumi Line –
(New) All lines are closed.
Hisatsu Line – Closed between Yatsushiro and Yoshimatsu.
Minamiaso Railway is closed.
Hisatsu Orange Line Railway is closed between Yatsushiro and Higo Tanoura.
Kumagawa Railroad is operating on regular schedules.
(New)Kumamoto City Tram is running as far as Kuwamizu/Shiminbyouinmae. Stops east of Kuwamizu are not in service.
(New)Kumamoto Electric Railway has suspended service due to electrical problems.
Road Transportation
The expressway is closed between Ueki and Yatsushiro.
No highway buses are running between Fukuoka and Kumamoto at the moment.
Limited service has been restored on Kyushu Sanko, Kumamoto Bus, Kumamoto City Bus lines.
Kumamoto Electric Bus is operating on regular schedules.
There are many local roads in the Uki, Aso, Kamimashiki, and Kikuchi areas that are currently unusable. Here is the link from Kumamoto Prefecture for information on closed local roads (Japanese only):
http://cyber.pref.kumamoto.jp/bousai/Content/asp/topics/topics_detail.asp?PageID=14&ID=1177&type=1
Route 57 between Kumamoto and Aso has been reopened, a detour road has been created around the earthquake affected areas.
Air Transportation
(New) Select flights are now arriving at Kumamoto Airport but all departing flights from Kumamoto have been cancelled for the day. This includes flights from ANA, JAL, Fuji Dream Airlines, and Solaseed Air.
(Update) Fuji Dream Airlines has announced they are restarting flights departing from Kumamoto as of today (4/19).
Supermarkets
Please note, many stores have limited stocks and may close once supply has run out.
Aeon:
Open – Aeon Nishiki, Aeon Amakusa
Partially open – Aeon Kikuyo, Aeon Yatsushiro, Aeon Kumamoto Chuo, Aeon Uki, Aeon Ozu
(New)Closed for repairs – Aeon Kumamoto
Kyushu Shinkansen:
On the evening of 14 April 2016, the entire length of the Kagoshima Route was shut down after the first of two powerful earthquakes struck Kumamoto prefecture. There was extensive damage along the route, including cracks in elevated support structures at 25 locations and collapsed sound insulation walls at 50 locations. 30 additional sound wall damages were reported by the transport ministry on 18 April.
A Series 800 consist that was deadheading derailed near Kumamoto Station after the first tremor. On 18 April, JR Kyushu began attempts to return the derailed train to the tracks.
The portion of the line between Shin-Minamata and Kagoshima-Chuo is scheduled to reopen on 20 April with services operating every 1-2 hours. The remainder of the line is closed and, according to the transport ministry, will not reopen in time for Japan's Golden Week holiday
