Some quick, first impressions of a few popular learning apps and courses for the Mandarin and Cantonese languages:
Mandarin
Pandanese - Nice-looking, simple and straightforward but fun way of learning characters, meaning, and reading.
Ninchanese - Feels like a full-blown language course that is presented in a friendly, good-looking, and well-organized way.
Skritter - A good way to learn how to write characters while learning the meaning and reading. The only downside is that it seems like you learn mostly by rote memorization and repeating lessons.
Chineasy - Fun and extremely well-designed way of learning characters, meaning, and reading, but apparently sometimes inaccurate and highly selective of certain words and phrases.
HelloChinese - Kind of a hybrid of Chineasy and Ninchanese. Lessons presented in a very well-designed way but with a look towards a more long-form course rather than to quickly learn some small words or phrases here and there.
Cantonese
Ling - Drops you right into learning typical phrases and giving examples of conversations in a fun, well-presented way. Might be a bit too advanced to start with, though.
CantoneseClass101 - A very formal, albeit modern language course on Cantonese. Gives audio lessons and lots of text to read through and digest. Comprehensive but also completely self-led and thus no feedback or reinforcement except for from yourself (unless you pay extra).
CantonSkill - Good app with simple, well-reinforced lessons that includes speech Recognition for making sure you are pronouncing words correctly. Great for learning and better than most but production value is not as high as some other apps.
Drops - Extremely well-designed, pictograph-based learning app. Bite-sized, five minute lessons that teach and reinforce words quickly. Might be better for just relating sound to meaning, though, than anything else.