Amin Raoufi

Admin Toolbar Live Clock keeps the current site time always in view while you work.
<blockquote>
Perfect for distributed editorial teams, agencies running sites in different time-zones, or any admin who regularly checks cron jobs, comment timestamps or scheduled posts.
</blockquote>
<h3>Who benefits?</h3>
<ul>
<li>Editors coordinating global content releases </li>
<li>Support agents logging activity against server time </li>
<li>Developers verifying scheduled tasks (Cron / Action Scheduler) </li>
<li>Multisite super-admins overseeing sites across regions </li>
</ul>
<h3>Feature highlights</h3>
<ul>
<li>Live ticking – updates every second; no page reloads, no Ajax polling </li>
<li>Calendars – Gregorian, Persian (Jalali), Islamic (Hijri), Hebrew, Buddhist (Thai) and Japanese </li>
<li>Languages bundled – English (en_US), فارسی (fa_IR), العربية (ar_SA), Español (es_ES), Français (fr_FR), עברית (he_IL), हिन्दी (hi_IN), 日本語 (ja_JP), ไทย (th_TH) (+ fully translatable via PO/MO files)</li>
<li>Time formats – 12-hour or 24-hour </li>
<li>Per-user timezone – keep the site setting or pick any IANA timezone </li>
<li>Colour-picker – separate, native WP colour-picker fields for clock & date </li>
<li>Admin-only & WPCS – assets load only in wp-admin for users with manage_options; codebase follows WordPress-Coding-Standards </li>
<li>Clean uninstall – removes all options on Delete via <code>uninstall.php</code> </li>
</ul>
Find the settings page at Dashboard → Settings → Toolbar Clock.

Admin Toolbar Live Clock

Real-time clock for the admin toolbar with multi-calendar, per-user timezone and colour controls.

Ben Lobaugh (blobaugh)

<ul>
<li>NOTE: Much of this functionality is built-into the user profile now. Be sure to look there before installing this plugin as it may no longer be necessary with your version of WordPress</li>
</ul>
As of version 3.3.1 of WordPress the toolbar is required everywhere when a user is logged in. 
This behavior is not always desired, especial during design phases of development. 
There may also be client requirements against having the toolbar show on the front. 
With this plugin you will be able to turn on/off the toolbar per user via the profile page *.
<ul>
<li>This functionality still in development. Currently it will remove the frontend toolbar only.</li>
</ul>

Remove Toolbar

Remove the new toolbar on a per user basis for both the front-end and back-end

Admin Toolbar Live Clock vs Remove Toolbar