I found a solution!
Thanks to jgorkos on the Ubuntu Forums:
Re: Samsung Galaxy i9000 not recognized
I struggled with this too. There is one step left on the phone after you plug it in that you need to take.
Here's how I got it to work, using Lucid Lynx Kubuntu. Surely a Gnome desktop will be similar.
1) On the phone, go to Settings->Applications->USB Settings and select the "Mass Storage" Options.
2) Go back to Settings->Applications->Development and select "Stay Awake"
3) Plug in your USB cable to the phone and computer.
The phone will say "USB Connected in the status bar at the top, and a USB symbol will appear.
4) Drag down the notification bar from the top and hit the "USB Connected: Select to copy files to/from your computer"
5) You get a new window with "USB Connected: You have connected your phone to your Computer via USB. Select "Mount" if you want to copy files between your computer and your phone's SD card." Select MOUNT.
6) Your notification applet on your computer will squawk about TWO new drives being attached. There will be a little one, and a big one. Mount the bigger of the two.
There will be a selection of existing directories/folders (if you think folders, stay off my lawn):
Android
Bluetooth
DCIM
kindle
mobi_drm
sd
slacker
twc-cache
If you want to add music, create a new directory (folder, youngster) called "Music" and copy your music into it.
Don't forget to use the device notification applet/command line/etc to unmount the drive when you're done copying.
7) Finally, drag down the notification bar on the phone again and hit "Turn off USB Storage" to tell the phone to stop making the SD card available to the host PC. After you confirm that, your card will be scanned for new media, and it will be available for your consumption via the Music Player.
Enjoy your new Galaxy S/Vibrant/Whatever your carrier calls it. I know I am.