Geoffrey

Since WordPress 4.5, that feature is included in the Core. You don’t need this plugin anymore. Thank you all for support.
Adds the possibility for users to log in with its email address OR its username. 
Uses native WordPress functions. 
Lightweight plugin, no options, just activate it and it works!
Please, use the support forum to tell me bugs encountered, before rating the plugin. Be patient, it’s free, remember it 😉
Languages available:
<ul>
<li>Deutsch</li>
<li>English</li>
<li>French</li>
<li>Spanish</li>
<li>Russian</li>
</ul>
<h3>Other plugins</h3>
Find my plugins at <a href="https://profiles.wordpress.org/creativejuiz/" rel="nofollow ugc">https://profiles.wordpress.org/creativejuiz/</a>

Juiz User Log-in by email

Allows users log in with its email address OR its username

NSquared

TylerDigital

scampanella

Simple Custom Login allows you to set a custom login for your WordPress site without any code.
Simple Custom Login allows you to: 
* Upload a background image – it fills the space on any device 
* Choose from basic color options – in case your image doesn’t look good with the default blue buttons & links
Make your login screen uniquely yours in under 2 minutes (no frustration necessary)
<h3>Usage</h3>
An options page can be found within Settings -> Simple Custom Login
Within the Simple Custom Login options page select the color scheme that you would like the button and link colors to be.
Upload a background image file that you would like to be used for the background of your WordPress login.
Be sure to Save Changes once you are done with your customizations.

Simple Custom Login

I love this plugin for adding some design to the default WordPress login. It's super simple to use and not too complex like Theme My Login can feel at times. tylerDIGITAL did a great job with this plugin!

Beautiful Login Screen and Easy to Use!

Quickly apply some fun or custom branding to your login screen

Juiz User Log-in by email vs Simple Custom Login