mrwulf

Completely integrated with the wordpress menu system so your theme’s menu menu styling is used.
Basic log in/out and register menu items that are only visible when appropriate.
Awesome custom menu item type will let you link to any page that requires the username as part of the url (example.com/members//messages). Tons of tags can be used to customize the menu text: 
* User Info: username, firstname, lastname, displayname 
* BuddyPress counts: unreadmessagecount, friendcount, groupcount 
* BuddyPress counts that hide when zero: (unreadmessagecount), (friendcount), (groupcount) 
* BuddyPress/WordPress avatar: avatar, avatar-thumb, avatar-mini
This plugin works great with “Menu Items Visibility Control” to only show menu items to certain roles/levels. 
Also, try “WP ToolBar Removal” to totally replace the ugly unthemed wordpress/buddypress menu.

BP Direct Menus

Add real menu items that go directly to buddypress pages! Add a profile dropdown with avatar, message counts, and more- fully customizable.

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.

BP Direct Menus vs Login Logout Menu