Eliminación de entradas de la base de datos a través de casillas de verificación

Aquí, se prueba y funciona mientras se usa mysqli_ en lugar de mysql_

Reemplace con sus propias credenciales.

Algunas cosas, su casilla de verificación necesitaba corchetes alrededor del elemento nombrado como mencioné en mis comentarios, es decir, name='checkbox[]' de lo contrario, recibiría un foreach no válido error de argumento.

Nota al margen:hay que formatear un poco, pero funciona.

<table class="ts">
        <tr>
            <th class="tg-031e" style='width:1px'>ID</th> 
            <th class="tg-031e">IP address</th>
            <th class="tg-031e">Date added</th>
            <th class="tg-031e">Reason</th>
        </tr>

<?php

$DB_HOST = "xxx";
$DB_NAME = "xxx";
$DB_USER = "xxx";
$DB_PASS = "xxx";

$con = new mysqli($DB_HOST, $DB_USER, $DB_PASS, $DB_NAME);
if($con->connect_errno > 0) {
  die('Connection failed [' . $con->connect_error . ']');
}

$SQL = "SELECT `ID`, `IPaddress`, `DateAdded`, `Reason` FROM `banned`";
$exec = mysqli_query($con,$SQL);

echo "<form method='post'>";

        while ($row = mysqli_fetch_array($exec)){
                echo "<tr class='tg-031h'>";
                echo "<td class='tg-031e'><input type='checkbox' name='checkbox[]' value='" . $row[ID] . "'></td>";

                echo "<td class='tg-031e'>" . $row['IPaddress'] . "</td>";
                echo "<td class='tg-031e'>" . $row['DateAdded'] . "</td>";
                echo "<td class='tg-031e'>" . $row['Reason'] . "</td>";
        }

echo "</tr></table>"; 

        echo "<input name='delete' type='submit' value='Delete'></form>";

        if (isset($_POST['delete']) && isset($_POST['checkbox'])) {
            foreach($_POST['checkbox'] as $id){
                $id = (int)$id;

                $delete = "DELETE FROM banned WHERE ID = $id"; 
                mysqli_query($con,$delete);
            }
        }

?>

Utilice mysqli_* con declaraciones preparadas , o PDO con declaraciones preparadas por esto.

Editar: mysql_ versión

<table class="ts">
        <tr>
            <th class="tg-031e" style='width:1px'>ID</th> 
            <th class="tg-031e">IP address</th>
            <th class="tg-031e">Date added</th>
            <th class="tg-031e">Reason</th>
        </tr>

<?php

include 'connect.php';

$SQL = "SELECT `ID`, `IPaddress`, `DateAdded`, `Reason` FROM `banned`";
$exec = mysql_query($SQL, $connection);

echo "<form method='post'>";

        while ($row = mysql_fetch_array($exec)){
                echo "<tr class='tg-031h'>";
                echo "<td class='tg-031e'><input type='checkbox' name='checkbox[]' value='" . $row[ID] . "'></td>";

                echo "<td class='tg-031e'>" . $row['IPaddress'] . "</td>";
                echo "<td class='tg-031e'>" . $row['DateAdded'] . "</td>";
                echo "<td class='tg-031e'>" . $row['Reason'] . "</td>";
        }

echo "</tr></table>"; 

        echo "<input name='delete' type='submit' value='Delete'></form>";

        if (isset($_POST['delete']) && isset($_POST['checkbox'])) {
            foreach($_POST['checkbox'] as $id){
                $id = (int)$id;

                $delete = "DELETE FROM banned WHERE ID = $id"; 
                mysql_query($delete);
            }
        }

?>