Are there sandbox apps that does not require the phone to be rooted? There are many sandbox apps such as Permissions Denied (which was mention in one of the post) that can effectively control the permissions that apps which are installed onto your phone.

However, they require the user to root their phone.

So, are there sandbox apps that does not require user to root their phones and at the same time, allow user to control what permission to be given to the apps.

Would appreciate if the apps can run in Android 2 and above.
That would be a contradiction in terms: In order to disable permissions on-the-fly, root permissions are required -- no way around that.

For non-root users, there's only a different approach: Take the .apk apart before installing, manipulate the Manifest (remove unwanted permission's requests), re-assemble the .apk, and then install the modified package. Unwanted side-effect: No direct updates, as the signature on the package breaks this way. An app doing this is e.g. apktool, available for Windows, Mac and Linux.