Find and remove this bit of code from your navbar template.
<!-- breadcrumb, login, pm info -->
<table class="tborder" cellpadding="$stylevar[cellpadding]" cellspacing="$stylevar[cellspacing]" border="0" width="100%" align="center">
<tr>
<td class="alt1" width="100%">
<if condition="is_array($navbits)">
<table cellpadding="0" cellspacing="0" border="0">
<tr valign="bottom">
<td><a href="#" onclick="history.back(1); return false;"><img src="$stylevar[imgdir_misc]/navbits_start.gif" alt="$vbphrase[go_back]" border="0" /></a></td>
<td> </td>
<td width="100%"><span class="navbar"><a href="$vboptions[forumhome].php$session[sessionurl_q]" accesskey="1">$vboptions[bbtitle]</a></span> $navbits[breadcrumb]</td>
</tr>
<tr>
<td class="navbar" style="font-size:10pt; padding-top:1px" colspan="3"><if condition="$_SERVER['REQUEST_METHOD'] == 'POST'"><img class="inlineimg" src="$stylevar[imgdir_misc]/navbits_finallink_$stylevar[textdirection].gif" alt="" border="0" /><else /><a href="$navbar_reloadurl"><img class="inlineimg" src="$stylevar[imgdir_misc]/navbits_finallink_$stylevar[textdirection].gif" alt="$vbphrase[reload_this_page]" border="0" /></a></if> <strong>$navbits[lastelement]</strong></td>
</tr>
</table>
<else />
<div class="navbar" style="font-size:10pt"><a href="$vboptions[forumhome].php$session[sessionurl_q]" accesskey="1"><img class="inlineimg" src="$stylevar[imgdir_misc]/navbits_start.gif" alt="" border="0" /></a> <strong>$vboptions[bbtitle]</strong></div>
</if>
</td>
<if condition="$show['member']">
<td class="alt2" nowrap="nowrap">
<div class="smallfont">
<strong><phrase 1="$bbuserinfo[username]" 2="member.php?$session[sessionurl]u=$bbuserinfo[userid]">$vbphrase[welcome_x_link_y]</phrase></strong><br />
<phrase 1="$pmbox[lastvisitdate]" 2="$pmbox[lastvisittime]">$vbphrase[last_visited_x_at_y]</phrase>
<if condition="$show['notifications']">
<div><span id="notifications"><a href="usercp.php$session[sessionurl_q]">$vbphrase[your_notifications]:</a> <strong>$notifications_total</strong></span></div>
<if condition="$show['popups']">
<script type="text/javascript"> vBmenu.register("notifications"); </script>
<else />
<script type="text/javascript" src="clientscript/vbulletin_notifications_nopopups.js?v=$vboptions[simpleversion]"></script>
<script type="text/javascript"> vBulletin.register_control("vB_Notifications_NoPopups", "notifications"); </script>
</if>
<else /><if condition="$show['pmstats']">
<div><phrase 1="$vbphrase[unread_x_nav_compiled]" 2="$vbphrase[total_x_nav_compiled]" 3="$session[sessionurl_q]">$vbphrase[private_messages_nav]</phrase></div>
</if></if>
<if condition="$show['pmwarning']"><div><strong><phrase 1="$vbphrase[pmpercent_nav_compiled]">$vbphrase[your_pm_box_is_x_full]</phrase></strong></div></if>
</div>
</td>
<else />
<td class="alt2" nowrap="nowrap" style="padding:0px">
<!-- login form -->
<form action="login.php?do=login" method="post" onsubmit="md5hash(vb_login_password, vb_login_md5password, vb_login_md5password_utf, $show[nopasswordempty])">
<script type="text/javascript" src="clientscript/vbulletin_md5.js?v=$vboptions[simpleversion]"></script>
<table cellpadding="0" cellspacing="$stylevar[formspacer]" border="0">
<tr>
<td class="smallfont" style="white-space: nowrap;"><label for="navbar_username">$vbphrase[username]</label></td>
<td><input type="text" class="bginput" style="font-size: 11px" name="vb_login_username" id="navbar_username" size="10" accesskey="u" tabindex="101" value="$vbphrase[username]" onfocus="if (this.value == '$vbphrase[username]') this.value = '';" /></td>
<td class="smallfont" nowrap="nowrap"><label for="cb_cookieuser_navbar"><input type="checkbox" name="cookieuser" value="1" tabindex="103" id="cb_cookieuser_navbar" accesskey="c" />$vbphrase[remember_me]</label></td>
</tr>
<tr>
<td class="smallfont"><label for="navbar_password">$vbphrase[password]</label></td>
<td><input type="password" class="bginput" style="font-size: 11px" name="vb_login_password" id="navbar_password" size="10" tabindex="102" /></td>
<td><input type="submit" class="button" value="$vbphrase[log_in]" tabindex="104" title="$vbphrase[enter_username_to_login_or_register]" accesskey="s" /></td>
</tr>
</table>
<input type="hidden" name="s" value="$session[sessionhash]" />
<input type="hidden" name="securitytoken" value="$bbuserinfo[securitytoken]" />
<input type="hidden" name="do" value="login" />
<input type="hidden" name="vb_login_md5password" />
<input type="hidden" name="vb_login_md5password_utf" />
</form>
<!-- / login form -->
</td>
</if>
</tr>
</table>
<!-- / breadcrumb, login, pm info -->Then add it to the beginning of your header template.