I have any iPhone running iOS 5 or iOS 6:
Not right now. Check back for updates.
I have an iPhone 4 on iOS 4.1 through iOS 4.3:
Nope. Maybe later?
I have an iPhone 3G or 3GS on iOS 4.1, 4.2, or 4.3:
Yes, but complicated (and you lose GPS).
My device has never been past iOS 4.0.2.
If you upgraded while preserving your baseband (using PwnageTool, TinyUmbrella (only iPhone 4), or sn0wbreeze), then consider the last firmware you restored or upgraded to without custom tools (or, if you never restored, the firmware your device came with).