Have you tried using rs232 instead of SPI for the dosonchip?  This thing is on my wishlist, and I'm curious to see how well it works.  I think there's another vendor with a similar device, but I can't remember details (sorry).

I still have pc's with a RS232 interface. But no max232 or something like that to get the dosonchip voltages to rs232 levels.
I tried to get it going with a software serial port on the arduino but it didn't work.

One way to use SD/CF/etc is to simply use the SPI interface and use it as a chunk of flash memory.  Of course, you won't have a filesystem left so you can't just plug it in to a cardreader and grab a data file (although a linux user should be able to use dd to pull the entire contents off easily).

A trick I've heard about (but haven't tried) is to create a dummy file with junk in it, fighure out where that file starts on flash, then make sure you skip that many bytes (and don't write past the length of the file) when writing to the flash device.  I don't particularly like the sound of this, but it does have the potential of being the cheapest in terms of interface hardware and software development.

This sounds familiar. But I guess it will not be easy to get it working.

Then again, you can always implement FAT in arduino and share your hard work with the rest of us.  

I would love to do that. But it is maybe a little bit too much work for me.  No, to be honest: I don't think I am capable of doing such a job.

Is there anyone here using the arduino and storing data on a SD/CF card or USB stick or something like that? I have a dosonchip module that is not very cooperative. Unfortunately I read this thread http://www.sparkfun.com/cgi-bin/phpbb/viewtopic.php?t=5065 after ordering it. I tried to get it working with a softwareserial interface and at the moment I try to get it working with SPI but i am not really succesful. Documentation of this thing is minimal which makes it quite hard to get it working. So, I am looking for alternatives. I want something removable like a memorycard or USB stick. This thing: http://www.vinculum.com/prd_vdip1.html seems nice. But it is a new product and googling for it mostly gives the press release of his new product.

Does anyone know other alternatives?

Use something like the 74HC595, read this: http://www.arduino.cc/en/Tutorial/ShiftOut Or the max7219, use the search here on the forum to find some info.