The Google Authenticator project includes implementations of one-time passcode generators for several mobile platforms. One-time passcodes are generated using open standards developed by the Initiative for Open Authentication (OATH) (which is unrelated to OAuth).
This GitHub project is specifically for the Google Authenticator apps which target the Blackberry and iOS mobile platforms.
Other related Google Authenticator opensource projects can be found as noted below:
There are no account backups in any of the apps by design.
These apps are not on the app stores, and their code has diverged from what's in the app stores, so patches here won't necessarily show up in those versions.
Further documentation is available in the Wiki.