PDO implementation, MySQL, SQL Injection

Here's your example rewritten to use PDO, with explanations.

<?php
$username="********"; 
$password="*******";
$database="*******";

try {
  $pdo = new PDO("mysql:host=localhost;dbname=$database", $username, $password);
} catch (PDOException $e) {
  error_log("PDO connection error: " . $e->getMessage());
  header("Location: http://www.example.com/error.php");
  exit;
}

You can cast the GET parameter to int, which will just use the numeric part and strip off anything else.

$id = (int) $_GET['id']; 

Leave a placeholder in the query where you want to substitute the dynamic value. You can use either positional parameters with the ? symbol, or named parameters with the colon-prefix syntax.

$sql = "SELECT * FROM Videos WHERE id = :id";

It's important to test for error after every call to prepare() or execute().

It's best if errors don't simply die(), leaving the browser with a white-screen, but they should recover if possible, or else at least display a friendly "whoops!" page so the user can continue to use your site.

$stmt = $pdo->prepare($sql);
if ($stmt === false) {
  $err = $pdo->errorInfo();
  error_log("PDO prepare error: " . $err[2]);
  header("Location: http://www.example.com/error.php");
  exit;
}

Pass an array of parameter values to substitute as an argument to execute(). In the case of named parameters, it's an associative array. In the case of positional parameters, use a simple ordinal array.

if ($stmt->execute(array(":id"=>$id)) === false) {
  $err = $stmt->errorInfo();
  error_log("PDO execute error: " . $err[2]);
  header("Location: http://www.example.com/error.php");
  exit;
}

Then you can fetch an associative array per row from the statement's result set:

while ($row = $stmt->fetch(PDO::FETCH_ASSOC)) {
  extract($row);
}

Note I showed the use of extract(), which is a PHP builtin function that creates variables $title, $url, etc. based on the keys of the associative array $row. But I did this only to match your code; ordinarily I would just reference these fields as $row["title"] and so on.