The HD HERO Original camera, HD HERO 960 camera, and HD HERO2 camera do not have any built-in memory. You'll need to purchase one of the recommended SDHC cards to record photos and videos to.
The Standard Definition HERO cameras have 16 MB of built-in memory. This is good for about 25 photos, or a short video. You'll probably want to purchase an SD card so that you can save more shots.