Alessandro Raffa

In some cases you want your wordpress users to login with their email address instead of the username. To do this, you can use a good plugin like ‘WP Email Login’ or you can activate a ‘Register Plus Redux’ plugin’s option, but when the users will ask for lost password, the old / original username will be emailed to them, and this can cause confusion. To avoid this situation, just install and activate Login Email Sync, and it will sync the username ( user_login database field ) with the email ( user_email database field ) every time a user updates her/his profile.
If you find this plugin useful, please rate it.

Login Email Sync

In some cases you want your wordpress users to login with their email address instead of the username. To do this, you can use a good plugin like &#03 …

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 😉
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<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

Login Email Sync vs Juiz User Log-in by email