itzoovim

WordPress Login Box (WPLB) lets you add a log in/out box to your website.
WPLB includes an options panel which gives you control over your form.
Features:
<ul>
<li>Different styles</li>
<li>Highly customizable</li>
<li>Lightweight</li>
<li>Can be integreated with any theme</li>
<li>Works well with other plugins</li>
<li>Hackable</li>
</ul>
This plugin lets you choose custom links for a forgot your password page,and registration page. 
It also lets you choose a url that you users will be redirected to after they log-in/out. 
You can also enable the option to not redirect your users to WP-Login after failed login attempts! 
This plugins works well with other member plugins, and can help you create an overall better user experience.
You can view a sample <a href="http://itzoovim.com/plugins/customize-and-add-a-wordpress-login-form-to-your-site/#sample_wordpres_login_form" rel="nofollow ugc">wordpress login form</a> by visiting this link.
<h3>Requirements</h3>
In order to work, WPLB needs the following :
<ol>
<li>PHP version 5+</li>
<li>Preferably the latest version of WordPress.</li>
</ol>
<h3>Donations</h3>
We are still working on a donations link at the moment. For now, leaving a nice rating will be appreciated as well.

WP Login Box

Easily add a forum like log in/out form to your site.

Julio Potier

Grégory Viguier

With this plugin you can now add a real log in/logout item menu with autoswitch when user is logged in or not. 
Nonce token is present on logout item. 
2 titles, one for ‘log in’ and one for ‘logout’ can be set up. 
Also, you can set the redirecion page you want, just awesome.

Login Logout Menu

This plugin (still) works great.

However be aware that it's not compatible with PHP 8 or newer, the latest PHP version this plugin will work with is 7.4. This is due to its use of create_function, which has been deprecated since PHP 7.2 and removed as of PHP 8. This should be replaced with an anonymous function, which is easy enough. But I haven't tested this myself, so I don't know if that's the only incompatibility with PHP 8+.

Works great, but...

You can now add a correct login & logout link in your WP menus.

WP Login Box vs Login Logout Menu