I used "File Manager" (like Root Explorer) and re-named all the camera and video OGG audio files. I used to do this with CyanogenMod before they added the option to turn off the camera shutter sound within the app.
I renamed cam_start.ogg, cam_stop.ogg, camera_click.ogg, camera_click_short.ogg, shutter.ogg, shutter_multiple.ogg, and videorecord.ogg.
I simply replaced the OGG extension with OLD. No more camera sounds.
It should be noted that when Samsung releases an update, the files will be restored and you will have to go through the whole procedure again.
RandomKing's method is easier, but I wanted a way to restore the sound just in case.
- Samsung Galaxy S 4 (Sprint): Stock
- ASUS Transformer TF101: Official ASUS ICS 4.0.3 rooted using viperMOD PrimeTime v4.5
- Retired: HTC EVO running CyanogenMod 7.2.0 / Android 2.3.7 with Tiamat SBC+ kernel overclocked to a stable 1.3GHz
- Retired: Samsung Galaxy S 3 (Sprint): freeza's Odex Jelly Bean L710VPBLJ7