Jan Štětina

This plugin provides a simple API for storing miscellaneous log entries and their overview in admin area (or network 
admin area, if activated on a multisite).
Developed for private use (heavily used by my other plugins), but has perspective for more extensive usage. I can’t guarantee any support in the future nor further development, but it is to be expected. Kindly inform me about bugs, if you find any, or propose new features: <a href="mailto:zaantar@zaantar.eu?subject=[wordpress-logging-service]" rel="nofollow ugc">zaantar@zaantar.eu</a>.
See Usage and FAQ for more information.
<h3>API</h3>
Definitions:
<pre><code>WLS
</code></pre>
<ul>
<li>
should be checked before using any wls function
WLS_VERSION
</li>
<li>
should(!) contain current WLS version string
</li>
<li>
severity levels:
<pre><code>WLS_NOCATEGORY = 0

WLS_INFO = 1

WLS_NOTICE = 2

WLS_WARNING = 3

WLS_ERROR = 4

WLS_FATALERROR = 5
</code></pre>
</li>
</ul>
Functions:
<pre><code>wls_is_registered( $category_name );
</code></pre>
<ul>
<li>
returns <code>true</code>, if <code>$category_name</code> is registered
wls_register( $category_name, $description );
</li>
<li>
registers <code>$category_name</code> as a log category.
</li>
<li>
<code>$description</code> will be shown in admin area
wls_clear( $category_name );
</li>
<li>
deletes all log entries of category $category_name
wls_unregister( $category_name );
</li>
<li>
same as wls_clear & removes category $category_name from the list
wls_log( $category_name, $text, $user_id, $date, $blog_id, $severity = 0 );
</li>
<li>
inserts a new log entry into specified category
</li>
<li><code>$date</code> must be formated according to ISO 8601</li>
<li>
<code>$severity</code> should be one of defined severity levels (see above)
wls_simple_log( $log_name, $text, $severity = 0 );
</li>
<li>
equivalent to <code>wls_log( $category_name, $text, get_current_user_id(), date( 'c' ), get_current_blog_id(), $severity);</code>
</li>
</ul>

WordPress Logging Service

Provides a simple API for storing miscellaneous log entries and their overview in admin area.

tarppa

Write all login attempts where both username and password are supplied to a log file. The logfile is relative 
to error.log and is called ‘login.log’, the format : “TIMESTAMP USERNAME SUCCESS/FAILURE”.
In practice this plugin is a rewritten version of the wp_authenticate_username_password function from user.php and replaces 
it in the login process.

WP Login Logging

Write all login attempts to a logfile by replacing default wp_authenticate_username_password functionality

WordPress Logging Service vs WP Login Logging