Android: Free app SHEDroid really is like a shredder for Android phones. It doesn't perform a "secure delete" on a particular file or folder, but instead securely wipes the supposedly vacant spaces where deleted files used to be listed. If you're wondering why that means anything, it's because deleted files aren't really gone the moment you delete them — they're just not listed anymore. Something needs to be written over the data for it to really be gone, and that's what SHEDroid does with one tap of the finger.
Performing the wipe is nice, but SHEDroid's nicest feature is probably scheduled wiping. If you do a lot of document work on your phone, you can just have the app quietly running in the background, and wiping deleted data every few hours. The process only takes about two minutes, so it's not much of a burden to let it do its job — just don't try doing anything while it's working.