Final Cut Pro saves it's project files wherever you want it to. They can also get kinda big depending on the length and complexity of the project. There are all kinds of ways to automatically back up stuff on the Mac but one way I've come to really like is by using the free service provided by Mozy.com.
It's FREE 2+ Gig backup that runs automatically when you set it to. I have mine set to back up my FCP autosaves and my main project save files every night at 3am. To restore files it's as easy as hitting an item in your menubar or you can log in at their site and restore files.
What's great about Mozy is that it runs in the background, it's encrypted, they give you 2+ Gigs of room and it's FREE. Plus if you sign up using someone's referral number they get an extra 256MBs of storage for free.
Here's my referral number :)
One thing to be aware of is that the Mac Mozy client is still in beta. So far I haven't had any real trouble other than having to re-install it once but that was a few versions ago. Don't rely exclusively upon Mozy or any one backup solution, use at least two.
I for one, use Mozy, occasional CD/DVD data back up and dump save files to my portable flash drive.
One other quick method to back up files under 20MBs is to get a free Gmail account and mail them to yourself. Google archives everything forever it seems.