Starting April 6th, Xbox 360 users will be able to USB flash drives for storage.
Each flash drive can hold up to 16 GB of data including profiles, game saves, demos, and more. It is required that the flash drive has at least 1 GB of space.
The catch here is you have to dedicate space to your Xbox 360. Up to 16 GB can be configured for the Xbox 360. For example if you have a 32 GB flash drive, you can dedicate 16 GB to your Xbox 360, but still use the other 16 GB for your PC or whatever you want. According to Major Nelson, external hard drives might work as well, but you can still only make use of 16 GBs.
If you are too lazy to figure out the whole configuration process, Microsoft will be releasing a Xbox 360 branded USB flash drive in cooperation with Sandisk which is pre-configured for the system.