The Japanese Language Tools dictionaries are actually just documents in a standard Japanese dictionary and eBook format called EPWING. You can use them on any device as long as it lets you enter and display Japanese and has an EPWING reader program. I've personally used my dictionaries on Windows Mobile PDAs and phones (quite a few different models), Palm OS PDAs (ditto), Windows XP (desktop, notebook, and tablet), and the iPod Touch (works the same as iPhone and iPad). I've also tried out the Japanese input system in Android. I can give you some starters for those platforms; for the rest, you'll have to turn to the net for resources and instructions. As always, I recommend trying out some of my free dictionaries before buying a dictionary from me or anyone else.
Windows XP. Simply activate East Asian Language support and a Japanese IME from the control panel, if you haven't already, then install the excellent (and free!) program EBWin (scroll down to the middle of the page). One cool feature most people don't use: the IME pad. Using the mouse or, if you have it, a touchscreen or tablet, you can draw kanji in to enter them just like in the Windows Mobile systems I sell. Some tiny subnotebooks now come with touchscreens, making this feature even easier to use. I've got a Viliv X70EX tablet I just love for when I'm on the road--I admit, though, that I use a roll-up rubber USB keyboard instead of the onscreen virtual keyboard whenever I'm going to be typing more than a short note. I deliberately chose the XP version rather than the one with Windows 7 Starter for the reason mentioned below.
Windows Vista and Windows 7. Annoyingly, the excellent language support included for no extra cost in all versions of XP now comes only with Ultimate and better versions of Vista and 7 (though you can pay Microsoft extra to add it to lesser versions). However, folks online are reporting that you can install the Google Japanese IME onto the cheaper versions of Vista and 7--you should do some research online onto installing it onto your particular version of Vista or 7, though, because I haven't tried it myself and can't offer any guarantees (I welcome any information users can give me to pass along here, though). Google IME looks and works almost exactly the Japanese support that comes with XP, including the IME pad for handwriting entry (though the dictionary it uses is smaller, meaning it happens a bit more frequently that when you enter hiragana with the keyboard and hit the "convert to kanji" button, the word you're trying to enter doesn't appear--you then have to enter the word one kanji at a time). If you have Vista or 7, you can install Google IME and check it quite easily. Once you've got Japanese going, install EBWin as with XP and you're good to go! Windows 8, with its much improved touichscreen support, should also include excellent handwriting recognition--my guess is a Win8 tablet or touchscreen notebook will make the best platform yet for Japanese dictionaries (I'm sure you'll still have to upgrade to Ultimate or buy the Japanese version of lower versions to get Japanese support, though, just as in Vista and 7.
Mac OS X. OS X includes excellent Japanese support. As with XP, you just have to enable it from the settings. There are a few different choices for EPWING programs. The best is EBMac, from the maker of the EBPocket program used in JLT Complete Systems and on the iPhone. It's optimized for EPWING, so it's fast and efficient, it offers the complex search options that make EBPocket and EBWin so powerful, and it's compatible with the .ebz compressed EPWING format of the JLT dictionaries. Plus, it's free. It's a new program, so check back frequently for updates, a manual, and maybe an English-interface version if the current installer doesn't offer one. If you want to try something else, I don't know if all of the other Mac dictionary programs are compatible with the .ebz compressed EPWING format--if one doesn't work, try another. Here are a few I've found (but haven't tried): Kamonos (still available?), Kotonoko, Logophile (not free), and JEDict. There may be more.
Linux. I've seen enough to know it's out there, but you'll have to google it yourself. I don't know much about Linux.
Nokia Internet Tablets/Maemo. Ditto. It's there--but you'll have to go get it. I don't know how good the Japanese support is--whether there's handwriting entry or just a keyboard IME, and how well those systems work. My impression from what I saw a while ago is that Japanese support is fairly simple--limited keyboard IME. But there may be something better available now. Again, please check it out yourself before buying anything--my knowledge here is too shaky to base any decisions on.
Android. As in everything else, Android lets you do more and has much more power and potential than iOS (iPhone and iPad). Overall, if you're a pretty competent computer user--comfortable fooling around with settings and minor hacking--you'll get more out of Android. If you're still shopping for a device and you just want something that works right out of the box and never gives you any headaches, though, Android (as of November 2012) may not be for you.
As for Japanese entry, all the free keyboard Japanese input apps are still really primitive. When I enter even some fairly common words in hiragana, these apps often can't convert them to kanji. However, ATOK has released an Android version of its excellent Japanese input app. It includes a good virtual keyboard IME (also works with physical keyboards, either built-in or accessory) and a phone keypad-style IME. Unfortunately, it doesn't include the excellent handwriting recognition that its versions for regular Windows computers and old Windows Mobile computers included. As I write, ATOK for Android is 1500 yen. Now, the excellent EB Pocket Pro appdictionaries is also available for Android (600 yen for the pro version; definitely worth the upgrade from the free one). EBPocket Pro is the best Japanese dictionary program for two reasons. First, it can use any dictionary in EPWING format, including the JLT dictionaries, most major commercial dictionaries, and many free dictionaries; most dictionary apps either have an un-optimized version of Edict or a Japanese-to-Japanese dictionary (no English), and no other dictionary combines the depth and ease-of-use of the JLT version of Eijiro (without the JLT customization, it's useful mostly to native Japanese speakers using English, not the other way around). Second, EBPocket has powerful search tools that let you get the most out of massive resources like Eijiro. ATOK, EBPocket, and the JLT dictionaries give you the best Japanese dictionary system you can put on your 'droid--and if you don't need handwriting entry, you won't need anything else.
Great news on the Android front (updated november, 2012)! There's a new app adding much, much better handwriting recognition to Android devices that was possible before, and much better than anything for iPhone. It's called 7notes with Mazec. On a standard Android phone or tablet, it's much better than the previous best, HanWriting. It's more forgiving of stroke order and other mistakes and simply works better in every way, and it can directly enter text into any app--it works like a regular input method. It's still not ideal for use with a fingertip, but still makes an Android phone a much better Japanese dictionary than before (and much better than an iPhone). However, put 7notes with Mazec on a Samsung Galaxy Note, which has a special touchscreen that works with a fine-tipped stylus for easy, accurate, and precise Japanese handwriting recognition, add ATOK, EBPocket, and some JLT dictionaries, and you've got an absolutely fantastic Japanese dictionary system.
FYI, if you ever need to look up words with kanji you haven't learned yet, handwriting recognition is by far the best way to do it. Sometimes it's the only way to do it. If it works well, you can find such words quickly and easily; with less convenient or less effective versions, you can usually find what you need but it's a pain in the neck to do it often.
One important note about Japanese on Android, though--the built in fonts are biased toward Chinese, and some characters, although technically the same, look much different than they do in Japanese font. That means that however you enter a character, keyboard or handwriting, even if the system finds the correct character, it won't look like the one you were trying to enter and you might not recognize it. The 曜 [you] in 曜日[youbi] is a good example--in standard Japanese the top right part is ヨヨ (looks like two katakana yo characters), but in Chinese it looks the character for feather or wing, 羽 [hane]. A lot of Japanese characters actually do have parts that are supposed to look like 羽 instead of ヨヨ, so 曜 written that way looks like it quite plausibly could be a completely different kanji--for quite a while I thought it wasn't finding the right kanji. To fix this, you have to change the system font (it's not enough to change the font in a particular app). This requires you to first root (hack) your 'droid, then install a font changing app. I'm using Arial Unicode on my Galaxy Tab 10.1 now, but with different versions of Android and different screen sizes, you'll probably have to do a bit of trial and error to find a font that looks decent on your tablet or phone. 曜 is a good test--if it comes out looking Japanese in a font, then it's likely the font will show the proper Japanese versions of all the other kanji, too.
I've got 2 'droids, a Galaxy Tab 10.1 tablet (updated to ICS) and an HTC Inspire 4G phone (and, on the dark side, an iPhone). I'm constantly trawling Google Play and other app stores, as well as blogs and reviews, to try to keep on top of everything out there on Japanese for Android. I'm sure there's stuff I miss, but I do my best, and when I do find something worthwhile, you'll see it here. So you may want to book mark this page and take a look back here every once in a while.