Due - my favorite iPhone to-do app
Due is my most favorite todo app. I got it for free from Starbucks but I would totally pay for it. Here's why:
It does not let you forget a to-do item
The built-in iOS reminder app reminds you about a to-do item once, but never again. I often forget about a to-do because I don't check the notification area that often. Due will just set off a new notification every 5 minutes, until you either mark it done, or snooze it. You just can't ignore it even when the phone is in your pocket.
There were many times where this "nagging" behavior really forced me to work on important things instead of forgetting them.
Marking it done, or snoozing it is also easy but that's not too different from the built-in app.
Super easy due date/time entry
The entry UI is optimized for entering due dates quickly. You can tap to pick a pre-set, but customizable time of day, or add a time interval. You can even type the relative dates as you would talk to Siri.
On the other hand, the built-in reminder app has no way to set a relative (e.g., "in 50 days" instead of "Jan 25, 2015") due date in the UI. You must talk to Siri to do it which a no-go in a meeting.
Auto-import from the built-in app
The app is capable of importing the built-in app reminders so you can easily move from the built-in app to Due. There is also automatic import-and-delete feature so you can keep using Siri for setting reminders.