Saving data to an SD card memory module using an Arduino
There are also a couple of hardware solutions which should be usable with Arduino:


DOSonCHIP which is FAT32- and FAT16-compatible. It will be really cool when they update the firmware to support I²C. SparkFun also had a breakout board for it (now retired), but the page may be useful for further information.
4D systems makes micro-DRIVE. Also this OpenLog open source data logger seems to be available from SparkFun.
GHI Electronics had the uALFAT MicroSD Board (now discontinued). It has an easy I²C interface and also supports long filenames.