Japan public transport directions

There are numerous options available for transit directions in Japan however how many of them you can use will be limited by your language ability and your choice of device.

Mainstream Apps

Yahoo! Travel (Site – Japanese) iPhone [J], Android [J]
Internet connection required.
The site and apps themselves are all in Japanese however input can be made in English (your results will be displayed in Japanese). Timetable searching. After searching, 20 of your most recent search results are available offline (requires reconnection to the internet for a new search).

NAVITIME (Site – Japanese) iPhone [E, J], Android [E, J]
Internet connection required.
The site is in Japanese however the apps are available in either Japanese or English. Currently (2016 April) heavily promoted in Japan. Timetable searching and (with the paid service) can reroute you in the case of a service disruption.

乗換案内 (Site – Japanese, English) iPhone [J], Android [J]
Internet connection required.
As mentioned by @Kent, there is 乗換案内 by Jorudan. These is also an English mobile website if you have internet access and a Japanese mobile. Timetable searching.

駅すぱあと (Site – Japanese) iPhone [J], Android [J], PC[J]
Internet connection required for mobile apps. Desktop App requires internet access for timetable searches.
The site and apps are in Japanese. Instead of an online app, has a desktop app instead. This is by far the most comprehensive of the apps mentioned however the UI can be a bit difficult to use initially. Provides maps of lines of all rail providers across Japan as well as timetable searching.

Hyperdia (Site – Japanese, English) iPhone [E, J], Android [E, J]
Internet connection required.
Produced by Hitachi Systems. Both websites offer free searches however both the iPhone and Android app require a paid subsciption. The Android app costs US$2.99/Month or US$25.99/Year for both English/Japanese access. The iPhone app costs $1.99/Month for Japanese only, US$2.99/Month for English/Japanese, $16.99/Year for Japanese only and $25.99 /Year for English/Japanese. The iPhone app can be operated by voice. Both apps can search for Japan Rail pass usage areas / timetables. Timetable searching.

Google Maps (Site – Japanese, English) iPhone [E, J], Android [E, J]
Internet connection required.
For completeness sake I will include this one. Offers both English and Japanese searching directly as well as a map of the area (it is a map app after all). Doesn’t normally show service disruptions in a timely manner. Some searches may give abstract results especially when searching in English (for example searching for a somewhat rare place name may give results of stores in otherwise unrelated parts of Japan (and sometimes the world)).

Special Mention

駅.Locky (Site – Japanese) iPhone [J], Android [J]
Internet connection required for updates and initial installation only.
駅.Locky was designed and built by graduate students from Nagoya University. It is a crowd-sourced rail time-keeping app which whilst may not be able to tell you directions, it will be able to tell you the time (to the second) of the next train (in fact all trains throughout the day for the lines you have downloaded). The app only has a Japanese version.

Notes

All apps mentioned have at least a free version or trial although many have additional services for a fee. Also that all Mainstream Apps will feature (usually toggleable) Train, Bus, Shinkansen, Plane and Ferry services when you perform a search. There are many more services than the ones mentioned here.

I’ve found a combination of Hyperdia and Google maps to be the best bet. Hyperdia tells you what route is best a lot of the time, but google maps suggests better stations and, I found, gives excellent route direction. It helped a lot when I was lost in the Nagoya subway system.

Jorudan is a popular site in Japan, which also has an English interface.
Train, highway bus, and plane info is available.

HyperDia is an alternative to Google Maps for planning transit journeys in Japan.

From Wikivoyage:

For sorting through transport schedules and fares, Hitachi’s Hyperdia is an invaluable companion; it computes to-the-minute directions including connecting trains, as well as buses and planes

From a happy user on reddit:

The best Hyperdia routes never show on Google Maps

Over and over, I’m looking for routes from the place I’m going to be in Japan to nearby destinations, and Google Maps always routes a big U-shape out and back in using different trains, but Hyperdia gives a direct route. Does anybody else notice this? Maybe it’s just the local trains around this area that confuse Google. The train lines and stations are all on Google Maps, it just never seems to pick the most direct route as any of the choices listed.