The backends: qmail-popup, bincimap, and others
s/qmail includes a primitive but fast qmail-pop3d POP3 service with a front-end module qmail-popup making use of variety of authentication modules, depending, how to access the user's mails. Additionally, bincimapd can be used for IMAP4, or any other, like Dovecot, Cyrus IMAP, or Courier IMAP as long as those services understand the underlying structure of mails, typically given in the Maildir or mbox format.
Other formats to store the retrieved mails do exist, but are currently not supported by qmail-start or qmail-local. This is matter of change.