I think you can remove the login form by removing the following bit of code, but make a backup of the template first.
Code:
<li>
<script type="text/javascript" src="clientscript/vbulletin_md5.js?v={vb:raw vboptions.simpleversion}"></script>
<form action="login.php?{vb:raw session.sessionurl}do=login" method="post" onsubmit="md5hash(vb_login_password, vb_login_md5password, vb_login_md5password_utf, {vb:raw show.nopasswordempty})">
<fieldset id="logindetails" class="logindetails">
<div>
<div>
<input type="text" class="textbox default-value" name="vb_login_username" id="navbar_username" size="10" accesskey="u" tabindex="101" value="<vb:if condition="$username">{vb:raw username}<vb:else />{vb:rawphrase username}</vb:if>" onfocus="if (this.value == '<vb:if condition="$username">{vb:raw username}<vb:else />{vb:rawphrase username}</vb:if>'){this.value=''; this.style.color='black';}" onblur="if (this.value == '') {this.value='<vb:if condition="$username">{vb:raw username}<vb:else />{vb:rawphrase username}</vb:if>'; this.style.color='#828282';}"/>
<input type="password" class="textbox default-value" tabindex="102" name="vb_login_password" id="navbar_password" size="10" onfocus="this.style.color='black';" />
<input type="submit" class="loginbutton" tabindex="104" value="{vb:rawphrase log_in}" title="{vb:rawphrase enter_username_to_login_or_register}" accesskey="s" />
</div>
</div>
</fieldset>
<div id="remember" class="remember">
<label for="cb_cookieuser_navbar"><input type="checkbox" name="cookieuser" value="1" id="cb_cookieuser_navbar" class="cb_cookieuser_navbar" accesskey="c" tabindex="103" /> {vb:rawphrase remember_me}</label>
</div>
<input type="hidden" name="s" value="{vb:raw session.sessionhash}" />
<input type="hidden" name="securitytoken" value="{vb:raw 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>
</li>
What other options do you want removed?