AivarasFX

Plugin creates widget that displays simple horizontal login. 
If theme has registered sidebar on top, widget may be used to display Horizontal login for top of the page for webpage users.
Input boxes are aligned in horizontal way, not verticaly. For blog users there is no need to open wordpress login page to login.
If blog has WP-fb-autoconnect plugin installed, widget also displays Facebook connect button and allows users to connect using facebook credentials.

FX simple LoginLogout

Plugin displays simple horizontal login for top of the page. If WP-fb-autoconnect plugin installed users may connect using facebook credentials

Julio Potier

Grégory Viguier

SecuPress

This plugin forbids access to https://example.com/wp-login.php and creates new urls, like https://example.com/login or https://example.com/logout. 
This is a great way to limit bots trying to brute-force your login (trying to guess your login and password). Of course, the new URLs are easier to remember too.
Also remember: the use of this plugin does NOT exempt you to use a strong password. Moreover, never use “admin” as login, this is the first attempt for bots.
By the way, if you are looking for a complete security solution, take a look at <a href="https://wordpress.org/plugins/secupress/" rel="ugc">SecuPress</a>: Move Login is included inside.
<h4>Multisite</h4>
Yes! The plugin must be activated from your network. 
Note 1: this plugin deals only with <code>wp-login.php</code>, not with <code>wp-signup.php</code> nor with <code>wp-activate.php</code> (yet). That means https://example.com/register will still redirect to https://example.com/wp-signup.php. I think this will be the next step though, but no ETA. 
Note 2: if users/sites registrations are open, you shouldn’t use this plugin yet. There are some places where the log in address is hard coded and not filterable. A <a href="https://core.trac.wordpress.org/ticket/31495" title="Always use 'login' as $scheme parameter for "login-ish" URLs, and other inconsistencies" rel="nofollow ugc">bug ticket</a> is open.
<h4>Requirements</h4>
<ul>
<li>You will need a FTP access: if the <code>.htaccess</code>/<code>web.config</code> file is not writable (you will need to add the given rules manually), or if something is wrong and you can’t log in anymore (see the FAQ in that case).</li>
<li>Should work on IIS7+ servers but not tested (I guess you should probably save a copy of your <code>web.config</code> file before the plugin activation).</li>
<li>For Nginx servers, the rewrite rules are not written automatically of course, but they are provided as information in the plugin settings page.</li>
</ul>

Move Login

Don't know why I didn't find "Move Login" first. I already tested 2 alternative free plugins and it was deficient in different ways.  "Move Login" is powerful, light and easy to set up. Very nice find. Thanks.

The best of the 3 ones I tested

Change your login URL for something like https://example.com/login and stop login brute-force attempts.

FX simple LoginLogout vs Move Login