You can create folders on your iPhone and file mail in to them, but there is no way to sync the folders present on the Verizon server. POP3 access only works for the Inbox.
Verizon would need to implement IMAP in order for that functionality to work.
I have started to use GMAIL so I can accomplish that. As one of the other posters indicated VZ would need to be using IMAP mail like GMAIL.