Using off the shelf hardware I have set up a pretty portable USBHostFS server for the PSP.
It can use any USB Mass Storage device including Thumbdrives, USB HDD's, IPods, and with a little tweaking Multi-Card readers. It also functions as a network file server.
It can be powered by a battery pack, though you would have to build one or use a commercial one.
My whole setup, NSLU2 & AC adapter, 160GB HDD, and Power pack all fit in a small bag. It runs for about 1 1/2 hours with the battery pack I'm using.
I have only seen a little lagging, but haven't tried many games.
For more info check the Readme.
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What you will need:
LinkSys NSLU2
This is a small file server for USB drives with 2 USB ports and an Ethernet port.
Note: this product has been discontinued by Linksys, but you can find it easily.
Unslung Firmware
This is an aftermarket Linux firmware for the NSLU2. It allows a lot more versatility for the device making it an excellent project platform. Other uses for Unslung include using USB devices over the network, sending infrared signals (like remote controls) over the network, Media servers, and many others.
SerComm Utility
Used to flash the firmware
Any USB Mass Storage device
USBHostFS for NSLU2 (With this guide)
Optional:
A battery pack or other portable power source. I am using a Black and Decker 20W battery/inverter.
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DISCLAIMER: You take all responsibility if you brick the NSLU2 doing this. You will replace the firmware with an after market firmware. This will void your warranty.
EDIT - Updated package to fix an issue with the install script. Thanks bigdaddie for finding it!