Get the imapsync utility at https://fedorahosted.org/imapsync/

This was a successful attempt to copy all my email from my old dovecot powered server up to gmail using imapsync

imapsync --host1 10.11.12.13 \
--authmech1 LOGIN \
--port1 993 \
--ssl1 \
--user1 fromusername \
--password1 fromimapmailpassword \
--ssl2 \
--host2 imap.gmail.com \
--authmech2 LOGIN \
--port2 993 \
--user2 [email protected] \
--noauthmd5 \
--password2  toimapmailpassword \
--prefix2 jmcd. \
--syncinternaldates

Where host1 and other *1 options are your source IMAP server and host2* and other *2 options are your GMAIL target.

--prefix2 allows you to copy the mail into a folder in gmail so you don't have dozens of messy folders littering the top level of your gmail mail account.