Since I'm a heavy Gmail user, my app of choice is Inbox for Gmail, and it's worked well at keeping my inbox manageable.
iPGMail is an app that implements the OpenPGP standard (RFC 4880, RFC 6637) and allows the user to create and manage both public and private (RSA, DSA, ECDSA) PGP keys and send and receive PGP encrypted messages.
iPGMail supports PGP key generation (RSA) directly in the app and stores them securely using the iOS keychain for the application. Using your own private PGP keys, you can encrypt and/or digitally sign any messages. Optionally, your public key can be attached to any message you send from the app so that the recipient can then import it into their own keychain, either on the phone or on any computer with PGP support.
A very highly rated app. It's biggest "trick" is that it integrates with over 55 other apps. For example:
Other apps it integrates with include: 1Password, Asana, AppigoTodo, 2 Days, 2Do, Appigo Todo, Asana, Box, Chrome, Clear, Dolphin Browser, DashPlus, Drafts, Droplr, Evernote, Facebook, Fantastical, Finish, Google Maps, Google Translate, HockeyApp, iCabMobile, Instapaper, Message, Mercury, Omnifocus, Pinner, Pinbook, Pinswift, Pushpin, Pocket, Pocket Informant, Readability, Reminder, Safari, Skype, The Hit List, Things, Trello, Todoist, Toodledo, Twitter, Wunderlist.
Boxer claims to be the fastest, most innovative email, calendar, and contacts app available for iPhone, and I'm not really about to argue with that. It offers support for Gmail, Outlook, Exchange (2007 and up), Yahoo, Hotmail, iCloud, & IMAP accounts.
Very powerful app.
myMail allows you to manage emails in your Gmail, Hotmail, Live, Outlook, Yahoo, MSN, iCloud and AOL email accounts at once.
Designed specifically to help you get through your email quicker and spend less time administrating your inbox.
If your email is littered with newsletters that you want to remain subscribed to but don't have the time to organize, then this could be the email client for you. Spark automatically determines if an email is a personal message, a newsletter, or just an automated notification.
CloudMagic has been designed to be simple, beautiful fast email. The app is available for iPhone, iPad, iPad Pro, Apple Watch and Mac OS X.
Compatible with Gmail, Exchange, Yahoo, Outlook/Hotmail, iCloud, Google Apps, Office 365 and any IMAP accounts.
Price: Free (with in-app purchases)
Triage isn't a true email client, instead it "is for people who struggle to stay on top of their inbox. It doesn't try to replace your desktop mail client, but lets you use your downtime to quickly remove the noise and stress."
When you sign in to your mail account, your new messages will appear as a stack of cards. Simply flick messages up to archive, or flick them down to keep in your inbox for later. You can also tap a message to view its full contents, and compose a short reply.
Triage supports Gmail, Yahoo! Mail, and iCloud Mail accounts, and most email services that support IMAP.
Who said Microsoft can't develop great apps for iOS? Outlook is one of the best - if not the best - mail apps for iOS out there. And don't let the Outlook name fool you, this app has nothing to do with the desktop application that man remember (usually with dread and hated).
Outlook for iOS works with Microsoft Exchange, Office 365, Outlook.com (including Hotmail and MSN), Gmail, Yahoo Mail, and iCloud.
Seamless inbox management
Easy access to calendar and files
Work on the go