Four learning and/or reference Android apps that work full screen on the eDGe.

Screenshots taken of the Android SDK emulator, v1.6 and scaled in the highest standard resolution to approximate the eDGe's 1024x600 (it came out 50-75 pixels less in each dimension). I have them running on my eDGe so I can confirm that this is how they look.
Aedict
Open source. Download the APK
here.

Based on Jim Breen's
WWWJDIC, this is a very handy Japanese-English dictionary app that accepts all types of input: romaji (roman alphabetic representation of the kana syllabary), English, Japanese (paste in the text), and handwriting-recognition kanji.
You can see that I input "neko" in the first screenshot. It could have instead been "cat" in the English input, either ねこ, ネコ, or 猫 in the Japanese input (that's hiragana, katakana, or kanji). For any of these the result would be the second screenshot.
The handwritten kanji recognition pad is very strict on stroke count and direction but forgiving with stroke order. The last stroke input is white and, as you can see in the third screenshot, I drew the last two strokes in the wrong order. Nevertheless screen four came up with the "correct" kanji as its first guess. I could then click on that result and get screen two.
This app is incredibly useful to have handy on the LCD screen while (attempting to) read a Japanese text or instructional material on the e-ink screen.
Ankidroid
Open source. Download the APK
here.

This is the Android version of the popular
Anki flash card system. On your PC (multiple OS's) you can build your own custom decks, or download one of the hundreds of decks made by other users. There are about a dozen versions for
Remembering the Kanji alone (I'm in the process of deciding which one to use). Unfortunately you can't search and download from Android. The decks need to be side-loaded.
Shown is the default Capitals of the World deck with the whiteboard activated. Draw the answer as I did with "Paris" to keep yourself honest (and for practice if the answer is a kanji character, for example).
The following two apps are currently only available through the Android Market, which only phones can access. Getting them off the Market and into the eDGe takes knowledge of the SDK. I include these for people who have that kind of skill and also in case they become more easily available (like, if enTourage gets their app store going).
Kanji Tutor
$1.99 on the Android Market. Home page
here.

This is a kanji drill app that covers the nearly 2000 most common Chinese characters in use in Japan. (The "jōyō" and "kyōiku" kanji.) The kanji are randomly selected from the "grade" selected in options, from 1-7.
Depending on drill choice, it will display a kanji and you have to click on the correct English meaning,
on or
kun reading, or it'll display the English meaning and you need to click on the correct kanji. Upon error the correct answer is shown briefly at the bottom in red. It also has a Lookup option to browse through kanji, see their readings and English meanings, or be directed by a link to the online Wiktionary for it.
This is good for building speed in recognition of what you already know. Not so much for learning. Simple but very nicely done. I don't regret spending the two bucks.
JLPT Kanji (demo)
Free on the Android Market for the demo (JLPT 4 only), non-free version covers all of JLPT 1-4. Homepage
here.

Android app for practicing kanji in preparation for the official Japanese Language Proficiency Test (JLPT). It is pretty much what you see on this one screen: a compact and nicely-made flash card system. Written kanji input is recognized and it'll change to red if you get it wrong, green if correct. The self-rating of 1-5 stars will determine how soon/often the kanji will repeat.
I'm not studying for the JLPT at this time so I probably won't use this much.
And that's it for now. I hope these mini-reviews are of aid to someone.