Are you rooted?
Titanium Backup has a free version and is generally considered the top app backup app.
AFAIK apps without root don't have read access to the storage of other apps... so I'd suggest you do it manually, but most android devices mount below the directory that stores the app data, and file browsers would need root to view it too.
Edit: Never mind guys problem solved! I just went ahead and downloaded the app because i thought.."well what do i have to loose?" and it worked, backed up an app i had and saved to the sd card.
Glad to see that you had some success. Have you tried to restore the app?
So did that backup app actually give you back an apk file, or just the folder of the program data that you need to restore with it?
I'm curious how it gets around the limits.
Ahhh, well at least you don't have to find and redownload the apps!
I use ES File Browser.
That's another good one. ES File Explorer is great and free. I've never used the APK backup part of it, but it's my de-facto file browser on Android. It handles Dropbox, Samba/Windows shares, FTP, too.
https://play.google.com/store/apps/details?id=com.estrongs.android.pop
ES File Explorer is one of the top most popular file browsers in the android market even i have it lol i didn't know it had a backup app feature i always just used it for moving and deleting files on my sdcard.