Please disclose any vulnerabilities found responsibly - report any security problems found to the maintainers privately.
PHPMailer versions prior to 5.2.14 (released November 2015) are vulnerable to CVE-2015-8476 an SMTP CRLF injection bug permitting arbitrary message sending.
PHPMailer versions prior to 5.2.10 (released May 2015) are vulnerable to CVE-2008-5619, a remote code execution vulnerability in the bundled html2text library. This file was removed in 5.2.10, so if you are using a version prior to that and make use of the html2text function, it's vitally important that you upgrade and remove this file.
PHPMailer versions prior to 2.0.7 and 2.2.1 are vulnerable to CVE-2012-0796, an email header injection attack.
Joomla 1.6.0 uses PHPMailer in an unsafe way, allowing it to reveal local file paths, reported in CVE-2011-3747.
PHPMailer didn't sanitise the $lang_path parameter in SetLanguage. This wasn't a problem in itself, but some apps (PHPClassifieds, ATutor) also failed to sanitise user-provided parameters passed to it, permitting semi-arbitrary local file inclusion, reported in CVE-2010-4914, CVE-2007-2021 and CVE-2006-5734.
PHPMailer 1.7.2 and earlier contained a possible DDoS vulnerability reported in CVE-2005-1807.
PHPMailer 1.7 and earlier (June 2003) have a possible vulnerability in the SendmailSend method where shell commands may not be sanitised. Reported in CVE-2007-3215.