Simple

$email = 'mail@example.com';
$validation = filter_var($email, FILTER_VALIDATE_EMAIL);

if ( $validation ) $output = 'proper email address';
else $output = 'wrong email address';

echo $output;

Advanced

This function doesn't only check if the format of the given email address is correct, it also performs a test if the host is existing.

<?php
$email="test@geemail.com";
if (isValidEmail($email))
{
       echo "Hooray! Adress is correct.";
}
else
{
       echo "Sorry! No way.";
}

//Check-Function
function isValidEmail($email)
{
       //Perform a basic syntax-Check
       //If this check fails, there's no need to continue
       if(!filter_var($email, FILTER_VALIDATE_EMAIL))
       {
               return false;
       }

       //extract host
       list($user, $host) = explode("@", $email);
       //check, if host is accessible
       if (!checkdnsrr($host, "MX") && !checkdnsrr($host, "A"))
       {
               return false;
       }

       return true;
}
?>

Regular Expression Test

function checkEmail($email) {
 if(preg_match("/^([a-zA-Z0-9])+([a-zA-Z0-9\._-])*@([a-zA-Z0-9_-])+([a-zA-Z0-9\._-]+)+$/",$email))
 {
    return true;
 }
 return false;
}

The above, with domain name validation:

function checkEmail($email) {
 if(preg_match("/^([a-zA-Z0-9])+([a-zA-Z0-9\._-])*@([a-zA-Z0-9_-])+([a-zA-Z0-9\._-]+)+$/",$email))
 {
    list($username,$domain)=split('@',$email);
    if(!checkdnsrr($domain,'MX')) {
        return false;
      }
 return true;
 }
 return false;
}