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

Nivardo Ch

Is your WordPress site protected against constant brute-force attacks? While strong passwords help, automated bots continuously try to breach your site through the login page. WPOrLogin offers a comprehensive solution to fortify your access points while ensuring a professional and branded user experience.
With the new Limit Login Attempts module, WPOrLogin tracks failed login attempts by IP address and automatically locks out the attacker for a specified duration, stopping brute-force attacks dead in their tracks. This is an essential layer of security that works alongside our popular reCAPTCHA integration.
WPOrLogin empowers you to take full control of the entire login and registration experience:
<ul>
<li>Security First: Implement Brute Force Protection and Google reCAPTCHA v2/v3 on all key forms (Login, Registration, Password Recovery).</li>
<li>Branding & Design: Easily customize the login page with your company logo, custom background, and brand colors.</li>
<li>User Flow Control: Redirect users based on custom settings after login or logout.</li>
<li>Clean Experience: Remove distracting elements like the language selector.</li>
</ul>
<h4>Key Security Features (New in 2.10!)</h4>
<ul>
<li>Brute Force Protection: Limits login attempts by tracking failed logins per IP address and automatically applying a temporary lockout.</li>
<li>Live Security Report: Provides an admin report with forensic data, showing currently blocked IPs, time of block, and geo-location links.</li>
<li>Smart UX Warnings: Displays a clear, dynamic warning to the user on their final attempt before lockout (UX Improvement).</li>
<li>Full Security Synchronization: Guarantees that the attempt counter is correctly reset upon a successful login, preventing legitimate users from being accidentally blocked.</li>
</ul>
<h4>Core Design & Utility Features</h4>
<ul>
<li>Custom Logo and Background: Change the logo and adjust the background image to your preference.</li>
<li>Predefined Layouts: Choose from multiple layouts (Basic, Standard, and Premium).</li>
<li>Google reCAPTCHA v2 and v3 Compatibility: Enhance security with reCAPTCHA verification options for login, registration, and password recovery forms.</li>
<li>Custom Redirection: Allows users to be redirected after login or logout.</li>
<li>Advanced Options: Remove the language selector from the login page.</li>
<li>Mobile-Friendly Design: Optimized layout for mobile screens.</li>
</ul>
<h4>Advanced Security with Google reCAPTCHA</h4>
Today, cyberattacks, especially automated ones, pose a major threat to website security. Among these attacks are bots attempting to access your site using stolen credentials or brute-force attacks. Google reCAPTCHA is one of the most effective tools for combating these attacks. With WPOrLogin, you can easily integrate Google reCAPTCHA v2 and v3 into your login, registration, and password recovery forms, adding an extra layer of security.
Protection for Key Forms:
WPOrLogin allows you to integrate Google reCAPTCHA in:
<ol>
<li>Login Form: Blocks unauthorized access attempts and brute-force attacks.</li>
<li>Registration Form: Prevents bots from creating fake accounts on your site.</li>
<li>Password Recovery Form: Protects against malicious password reset attempts.</li>
</ol>

Customize WordPress Login and Registration Page – WPOrLogin

Excelente

Protect your login page from brute-force attacks and bots while customizing its design with Limit Login Attempts, Google reCAPTCHA, and custom redirec …

Juiz User Log-in by email vs Customize WordPress Login and Registration Page – WPOrLogin