If you don't have an Eee PC, you can still run Linux from a humble USB flash disk, which will hold not only Linux but also your data. Several Linux distributions run from flash; here's how some of them compare.
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Of the two mini distros, I found DSL more useful because of the neater user interface and simpler install process. If you're looking for a complete Linux desktop on a USB flash disk, then Mandriva Flash is the clear winner. But if you don't want to spend money for your operating system, then you should consider Pendrivelinux.