I'm on the lookout for any decent self-study applications for my Google Android smartphone to help me brush up on my German on my daily commute. Can anyone recommend any for me?
Duolingo has a mostly decent android app.
It depends on what you want to train (grammar, vocabulary...) One of my favorites is the free trainer "King Of German Article".
It helps you to train nouns and the right gender with it. You can also train the different cases Nominativ, Akkusativ, Dativ. As for making grammatically right sentences you must know the right gender, this app helped me to improve my German a lot.
A trusty companion for any German learner, especially english, is the LEO dictionary, and they have quite a good Android App.
It's not an app to take up your spare time, but it is very handy for answering questions your have when you are out and about.
There are a lot of language learning apps for Android, it all depends on what you wish to focus on.
As far as flashcards go, AnkiDroid is my personal favorite. Anki is free for PCs, Mac, and Android (but not for iThings), highly customizable, but you'll need the desktop or web or make up for the features AnkiDroid misses. Still, spaced repetition is a decisive win.
With regards to reference apps, Duden has mobile apps, but I haven't used them myself. There's an app version of dict.leo.org, which I do use a lot (although the web interface would work just fine). Another reference app is the poorly named Deutsch Wörterbücher, which is a search portal that'll query a ton of different German-language reference sites if you don't want to bookmark them.
There seems to be a dearth of actual learning apps. DeutschAkademie is rather old-school and best suited for somebody well advanced who needs a refresher. German Class is very disappointing in terms of test coverage, although the vendor's apps for other languages (like English and French) are quite reasonable. I haven't tried the Babbel family of apps. Duolingo was mentioned before and it's probably one of the best language learning tools out there.
“LingoBrain” is a new game for learning German vocabulary (currently available for Android, but probably iOS soon too). It also includes a list of about 4000 words sorted by difficulty. It keeps track of your progress as you play and remembers which words you have difficulty with, allowing you to focus more on them.
There’s also a companion game for learning the Gender of German nouns.
I can recommend Goethe A1 Deutschtrainer. It contains several game sets, where you can learn german in a playful way.
I recommend using Learn German Fast By Yapping Puppy on google play. It covers lot of topic areas and has lots of German verbs conjugated. As well there are 2 games that come with it. Try it here for FREE at https://play.google.com/store/apps/details?id=com.yappingpuppy.com
Not a German-specific app, but with a podcast player like Google Player or PlayerFM you can listen to great German podcasts all day. My German has markedly improved from listening two hours a day on my commute - plus I have learned some Wissenschaft.
Memrise is such a wonderful app, you will learn 100 words within three days of time.