So, there you have it: a NAND-reader for 3.3V 8bit NAND flash chips for about EUR30 worth of components. It's not lightning fast or feature-rich yet, but it can be expanded to be. It was useful for me: I managed to read out the NAND chip I built it for.
The software (for Linux) is available, as usual, under the GPLv3. If you manage to upgrade it or make it faster, I'd appreciate a note. Update: some people already have been working on improvements, an example is Bjoern Kerlers work.
One last note: If you have a broken SD-card or USB-stick and think you can recover it using this, be warned: reading out the flash (with a tool like this) only is half the work. As soon as you have an image, you'll still need to know how to interpret it: most flash chips do bad block management and/or will swap sectors around for wear leveling. Unfortunately, I know of no free or cheap tool to undo that yet.