I guess I do not have to say anything about the standard apps, that come with iOS, so I will only talk about the ones, I bought/downloaded from the App Store:
Fantastical is a beautiful, highly usable calendar app, that uses natural language to create events and reminders. It also has a nice way to view all your appointments as a list and move from month to month very quickly.
Byword is my nvALT (on Mac OS X) equivalent on iOS. It contains and syncs all my notes via Dropbox, so everything is always up-to-date.
Tweetbot is the best Twitter client out there. ’nuff said.
OmniFocus is the most mission critical app, I have. It acts as my external brain. Without it, I am utterly screwed. All projects, todos and stuff, I must not forget, are in here.
1Password Did I say mission critical? My 1Password database contains more than a thousand entries. Beside my own passwords to various websites and online services, it includes passwords of client projects, secure notes, software licenses and much more. I can’t imagine a better way to organize, securely store and make all this information usable at the same time.
Pastebot is not even updated for the iPhone 5 – let alone iOS 7 – yet (which is a shame), it still works perfectly well. It allows you to sync your iOS’ devices pasteboard with your Mac via Wifi.
Pocket is my “read it later” service/app of choice. It makes it easy, to save articles on the web for offline reading. It is also integrated with lots of other apps and services.
Reeder is my RSS/feed reader of choice. I should probably upgrade to the latest version though…
WhatsApp is probably the most popular messaging app right now. Everybody uses it, so I guess I have no choice. Finally updated for iOS 7.
Launch Center Pro does so many things at once, I won’t go into any detail here. Just try this app and it will probably change the way, you use your iPhone.
Castro A new podcast client with a very nice and clean interface, that replaced Downcast as a my main podcast player. It has a very clean way of displaying available episodes. It also has a unique way of fast-forwarding/rewinding by scrubbing. I still like Downcast very much and it has much more advanced features, so give that a try as well.
Tell me about your favorite apps.