roggie

The WordPress “Meta” widget uses a lot of screen space and presents more information than some site designers would like. The Login/Logout plugin provides web designers with a compact alternative.
Available translations: English, French, German, Italian, Spanish, Catalan, Dutch, Polish, Norwegian and Persian.
The plugin can be used as a widget in themes that include sidebars. Alternatively, it can be added to your site’s footer or any other part of the site by inserting “rh_hype_lilo(); into your site’s PHP.
When the user is not logged in, the plugin presents a link so the user can Login, and an option allows another link to Register. Once logged in, users are redirected back to the page they came from. The plugin also displays the username and has an option to also display their email address.
There is also a link to Logout and, depending on the user’s role, a link to their profile or to the main site administration pages. Users are redirected back to the page they came from after they logout.
When used as a widget, a hyperlink option enables the widget to display an arbitrary number of hyperlinks to other sites/pages. These links are displayed only to logged in users. Other options enable the appearance of the widget to be customized to suit the theme design.
You must logout and in again to see changes such as new links etc. in the widget.
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Login-Logout

Adds simple, clean links so users can login/logout & register easily. Highly customisable, & can be used as a widget or inserted into your sit …

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.

Login-Logout vs Login Logout Menu