Backing up my 360 Save Games to USB stick

Yup, you can actually use up to a 16GB USB Storage Device for use with your XBox 360, assuming it has the software update that went out in Spring of 2010:

1. Connect the USB device to a USB port on your console.
2. Go to My Xbox, and then select System Settings.
3. Select Memory.
4. On the Storage Devices screen, select USB Storage Device.
5. Configure the storage device. You have two options for configuring your USB storage device for Xbox data storage:
   1. Erase all existing data, and configure the entire USB storage device.
   2. Configure some (but not all) of the USB storage device's memory (up to 16 GB).

For more information, have a look at the how-to guide on the XBox website: --> http://support.xbox.com/en-us/Pages/xbox-360/how-to/usb-flash-drive.aspx

Billy ONeal asked why there's an arbitrary 16GB limit. The official FAQ doesn't really address this, but instead tells you how grateful you should be ;-)

Why does Xbox 360 only support 16GB of storage, even though I have a much larger device?

Supporting USB storage devices up to 16GB in size is a huge increase in storage over any solid state memory storage solutions currently available for Xbox 360. Users that need more storage have options in the Xbox 360 hard drives, which are available for purchase separately.

However, it should be noted that you can use up to two USB Storage Devices, for a maximum of 32GB total size.