[Anonymous]

Little late on the response, but you could add this to your functions.php file – it makes a shortcode that shows a simple unsubscribe form:

Code can be found here: http://pastie.org/10496351

add_shortcode('newsletter_unsubscribe','hos_newsletter_unsubscribe');
function hos_newsletter_unsubscribe($atts) {
	
	extract(shortcode_atts(array(
		'class'	=> '',
	), $atts));

	$formcontent = '<script type="text/javascript">
		//<![CDATA[
		if (typeof newsletter_check !== "function") {
			window.newsletter_check = function (f) {
				var re = /^([a-zA-Z0-9_\.\-\+])+\@(([a-zA-Z0-9\-]{1,})+\.)+([a-zA-Z0-9]{2,})+$/;
				if (!re.test(f.elements["ne"].value)) {
					alert("The email is not correct");
					return false;
				}
				for (var i=1; i<20; i++) {
				if (f.elements["np" + i] && f.elements["np" + i].required && f.elements["np" + i].value == "") {
					alert("");
					return false;
				}
				}
				if (f.elements["ny"] && !f.elements["ny"].checked) {
					alert("You must accept the privacy statement");
					return false;
				}
				return true;
			}
		}
		//]]>;
		</script>
		<div class="newsletter newsletter-unsubscription">
		<form method="post" action="" onsubmit="return newsletter_check(this)" _lpchecked="1">
		
		<input type="hidden" name="form_action" value="unsubscribe">
		<table cellspacing="0" cellpadding="3" border="0">
		
		<!-- email -->
		<tbody><tr>
			<th>Email</th>
			<td align="left"><input class="newsletter-email" type="email" name="email_unsub" size="30" required=""></td>
		</tr>
		
		<tr>
			<td colspan="2" class="newsletter-td-submit">
				<input class="newsletter-submit" type="submit" value="Unsubscribe">
			</td>
		</tr>
		
		</tbody></table>
		</form>
		</div>';
	
	if( "unsubscribe" == $_POST['form_action']) {
		
		global $wpdb;
		$email = sanitize_email($_POST['email_unsub']);
		$result = $wpdb->query( $wpdb->prepare( 
			"DELETE FROM $wpdb->newsletter

			 WHERE /<code>email/</code> = %s
			",
				$email
			)
		);
		
		if( 1 == $result ) {
                        // Unsubscribe Message
			$content = '<h1>' . __('Successfully Unsubscribed','Newsletter') .'</h1>';
			$content .= '<p>' . __('You have been successfully unsubscribed from our newsletter.','Newsletter') . '</p>';
		} else {
			$content = '<h1>' . __('Unsubscribe','Newsletter') . '</h1>';
			$content .= '<p class="red">' . __('That email address was not found.','Newsletter') . '</p>';	
			$content .= $formcontent;		
		}
	} else {
		$content = '<h1>' . __('Unsubscribe','Newsletter') . '</h1>';
		$content .= $formcontent;
	}	
	
	return $content;
	
}

Then where you want the unsubscription form place this shortcode:

[newsletter_unsubscribe]

The Form:

[Author]

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