iOS Pick: Airmail
Leo Laporte's app cap on iOS Today 284 is Airmail for iPhone. This is an app for email, and has been around on the Mac for awhile already. Like many email apps, it has gesture support so you can act on your messages by swiping left or right on them. But it goes beyond that, with many powerful features including the ability to add messages to to-do lists, snooze them so they'll arrive later, move them to the trash or archive them, and much more.
Airmail has support for a wide variety of services including Google Drive, Dropbox, Pocket, OneDrive, Droplr, Box, Wunderlist, Github, and many more. There's also support for Apple Watch so you can triage email right from your wrist.