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

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A simple plugin that allows web developers and designers to brand the login page of WordPress for their customers.
You can upload a logo, background image, change colors and add custom CSS and JavaScriptto the wp-login.php form.

WP Custom Login Branding

A simple plugin that allows web developers and designers to brand the login page of WordPress for their customers.

Juiz User Log-in by email vs WP Custom Login Branding