I'd like to automate the process of locally backing up my Gmail account, and am looking for a solution that:
What resources are available for doing this in Ubuntu?
offlineimap 
is a popular solution for this.
After you install it create a .offlineimaprc
[general]
accounts = GMail
maxsyncaccounts = 3
[Account GMail]
localrepository = Local
remoterepository = Remote
autorefresh = 10 #refresh every 10 minutes
quick = 5 #Quick-syncs do not update if the only changes were to IMAP flags
[Repository Local]
type = Maildir
localfolders = /whatever/directory
[Repository Remote]
type = IMAP
remotehost = imap.gmail.com
remoteuser = your_username@gmail.com
remotepass = your_password
ssl = yes
maxconnections = 1
#Setting realdelete = yes will Really Delete email from the server.
#Otherwise "deleting" a message will just remove any labels and
#retain the message in the All Mail folder.
realdelete = no
Then you need to run offlineimap.
In some cases having offlineimap running all the time can consume large amounts of memory, especially if you have a large mailbox, so you can add an offlineimap check into cron to just check it and then exit, here's a daily backup:
@daily offlineimap -u Noninteractive.Basic
The files will be in whatever you define in the localfolders line as a Maildir. You can back this up using whatever backup method you use:
An alternative would be to use fetchmail. fetchmail can use both pop3s and imap4s to access Google. There are online tutorials on how to configure.
I have done some research on HOW TO backup an IMAP account comparing different available tools w.r.t. a set of wanted features and concerns. As a result, I used offlineimap, as already suggested above. (My saved comparison still may be useful to see a bigger picture.) Also, I summed up (answering a related question) some points concerning the architecture of such a solution for backing up an IMAP account and storing it in Git.
