Can you be clearer what you mean by "it doesn't work"? It won't send an email (ie you get an error message)? It sends OK but it's it received? It's received but goes into spam?
PHPmailer will fall back to the PHP mail() function if you're not using SMTP. However, the mail() function can be quite unreliable, many email providers will mark email as spam unless you have all the relevant MX records, SPF, DKIM (I think those are the correct acronyms!) etc.
