This digital camera supports an SD|SDHC|SDXC compatible memory cards, which is typical of many cameras of this age and type. SD cards are by far the most common type of memory card. They are compatible with the majority of digital cameras.
There are a number of other cameras that support an SD|SDHC|SDXC memory currently available which you might also want to look at including the Fujifilm X10, or the Canon SX280 HS which has better reviews.
If the memory card type of this camera is not good enough for you then you might also want to consider the Sony DSC-H400 ($226.97) (MicroSD (TransFlash)|MicroSDHC|MicroSDXC|MS Duo|MS Micro (M2)|MS PRO Duo|MS PRO Duo HS|MS Pro-HG Duo|MS XC-HG Duo|SD|SDHC|SDXC).