What you need to do here is escape the single quote in your string so that the database treats in literally. Here's one way to do it:
$string = "Can't get this in the DB";
$string = htmlspecialchars($string, ENT_QUOTES);
The single quote is converted to ' (i think this is its ascii code?). Now you should be ok for inserting into the DB. When you retrieve it from the DB PHP will know to convert the ascii code back to the single quote. For more info on htmlspecialchars() go to www.php.net and do a search in their function list. You also might wanna check out htmlentities().