It can be done. Generally. See e.g. the functions in avrlib http://hubbard.engr.scu.edu/avr/avrlib/ (it's even allready in a subfolder of the arduino package!)
Or a very nice MMC/SDC C library for AVR micros over here: http://ulrichradig.de/ (sorry, german only)
But if you want to read the card directly on a computer as a standard mass storage device, you have to wirte the data in a certain filesystem description. Something like FAT16, FAT32 etc. I'm pretty shure the Atmega8 has to less flash memory space and RAM for that... I saw working projects with Atmega32's and up, though. (i.e. on the hardware side, FAT filesystem is possible with the wiring board)
Alternatively, you can write your own simple data format. But this requires a custom software, if you want to read the data back on a computer.
Well, all depends on what you want to do with the card, when the data is written. What kind of data will you collect and why on a MMC card?
Oli