If you want to upload a profile photo to your Google Profile and use the cropping feature to edit the photo, it's important to know that the original version is publicly available. François Beaufort noticed that you can go to http://profiles.google.com/s2/photos/profile/me (replace me with the profile ID) and get the highest resolution of the profile picture as it was uploaded by the user.
When you upload a photo, Google says that "the full photo will be stored in your profile photos album, but we will display just the square crop on your profile page." By default, the profile photos album is not publicly accessible so it was reasonable to assume that the original photos can't be accessed by anyone but you. (Update: As Brian Rose points out, the profile photos album is unlisted if you haven't connected Picasa Web with Google Profiles and it's public otherwise.)
Until Google fixes this issue, it's probably a good idea to use a photo editor to crop and resize the image before uploading it to Google Profiles.
Android 7.1.2 Beta finally hits the Nexus 6P
43 minutes ago