Yes that's a good idea. But what's wrong is that you forgot the right closing parenthesis after the $email - the end part of VALUES().
The "password" is a MySQL reserved keyword and should not be used as a column name. Either change that column name to something else (which is what I recommend) to avoid further confusion, or enclose the column name inside backtick marks. Example:
$result = mysql_query("INSERT INTO users (username, `password`, email) VALUES ('$username', '$password', '$email')")
or die(mysql_error()." - Please contact the administrator.");