Platforms: iOS, Android
Finding a dictionary app with most of the features you need is difficult. Merriam-Webster's Dictionary, however, is an app that solves every avid bookworm's problems about finding a good dictionary app.
It comes with the prerequisites you'd expect from a dictionary app: well-defined words and examples to give you an idea on how they're often used. However, MW's Dictionary also has additional features that make it stand out.
Each word has two definitions: a quick-one, and a “full definition”, after which comes at least two examples. It is then followed by the origin of the word, its first usage, synonyms and, if the word allows for it, antonyms. These things come free and offline as well. Along with these features, the app also includes a “word of the day” as well as a few word-games, which are actually quite fun. You also have the option of liking a word, which is then added to your favourites list.
The only gripes I might have with this are that it comes with ads and the pronunciation of the word is only available when you're online. Other than that, with its numerous offline features, nice format and easy UI, this is definitely worth the download.