MyMail (iOS|Android) is a free e-mail client available on both Android and iOS that -- in addition to incorporating popular e-mail services -- lets you also create a free My.com account with unlimited storage.
The app has all the basic features of an email client, but unless you plan on switching your e-mail provider to My.com, it's hard to find a compelling reason to use MyMail in lieu of stock e-mail apps on either iOS or Android.
Adding an email account to MyMail is exactly like you'd expect: you tap on a provider, enter your credentials, and voila, your account is added to the app. As mentioned above, you're able to add an existing Gmail, Yahoo!, Outlook, AOL, or Hotmail account. Have an unlisted e-mail provider? MyMail allows you to enter your credentials and it will attempt to set up the account for you. As a test, I entered my iCloud e-mail address and MyMail successfully set it up within a few seconds.
Or if you'd like, you can sign up for a free My.com e-mail address. My.com's offering gives you unlimited storage and does away with a password based log-in. Instead, during the sign up process, you link your phone number to your username. Signing into your account requires that you enter a username, phone number, and a short code sent via text to your number. Without all three items, you can't access your My.com account. It's a novel, but effective approach not much different than two-step authentication.
Viewing, managing e-mail
Managing email is carried out through a series of gestures and taps. Sliding a finger across an email preview reveals a hidden menu where you'll find icons for read/unread, flag, file, mark as spam, or delete. Tapping the avatar next to a message enables multiple selection, where you can then perform the same action on multiple messages. Interaction with both mailboxes and messages alike is intuitive, and free of any issues. Searching email on a server is something a lot of third-party clients lack, yet MyMail does it exceptionally well, taking a few seconds to return any results.