1. GoodTask ($4.99 Universal) - A very clean UI that manages tasks and interfaces with native iOS Reminders. If you complete a task in GoodTask it will be marked as complete in Reminders and any other application that interfaces with the iOS Reminders database. Likewise, updates in other apps for reminders show up in GoodTask. GoodTask also shows a calendar view that allows you to select to display Calendar events as well, although in a read only mode. While I don't use GoodTask to enter reminders often (I primarily use Siri or use location based, more below), it does offer a better UI for task entry and updates than Apple's Reminders app.
2. Checkmark 2 ($5.99 iPhone) - Yet another task manager app for iOS. However, this particular one does something magnitudes better than Apple's Reminders or any other task manager app, location based reminders. By far the most accurate location based reminder app that I have used. In Checkmark, you can define various locations and set reminders to provide a push notification when you either arrive or depart the location. If you need to be reminded to do something based on a location, Checkmark 2 is the app to have.
3. Dark Sky ($3.99 - Universal) - The quintessential rain-alert weather app has finally landed a spot on my home screen, on the dock nonetheless! The precipitation push notifications and precise location identification have been spot on with when it will rain in the area I am located.
iPad
1. Good (Free - Universal) - The corporate email standard has finally made its way onto my iPad home screen. The larger iPad screen and split screen view within the application make email reading and composure a breeze.
2. GoodNotes 4 ($5.99 - Universal) - A very good and full-featured note taking application that specializes primarily on handwritten notes. GoodNotes is certified to work with the Jot Script stylus, which I have picked up to be my daily driver for note taking at work. The application works very smoothly with the Jot Script and takes note writing and digital whiteboarding to the next level on the iPad. Notes are saved to iCloud and can be backed up using DropBox.