I have seen examples (including code) on the web of AVR's using either MMS or SD cards directly.  The code would be less processing and more straight C though it should be possibile to integrate within the Arduino environment if space would permit.

Using an MMC card with SPI interface is fairly straightforward.  Most of the effort is if you want to read the MMC card a "hard drive" on a computer.  Than you have to replicate the FAT16/FAT32 filesystem on the card.  If you just write block data and either read it with the arduino hardware (or as a linux block device) it should be pretty easy.

If you want a canned FAT16/32 solution I know that Sparkfun sells a breakout board that can take serial (TTL RS232) commands and create computer readable files.  I have one and haven't done more than look at it yet.  The biggest drawback to it from the arduino environment would be that it needs RTS/CTS control signals to be implemented.