Is it possible to upgrade, without rooting, to a version not specifically released for the device? I have inherited an Android mobile and would like to upgrade it to the latest version of Android. Having come across posts such as is it possible to upgrade the android OS on all phones?, it appears I won't be able to. However, I am unsure what the definition of carrier is especially if the phone has been imported from overseas. Is there a way I could upgrade without jailbreaking the mobile phone? My question is applicable to all mobile phones running Android.
Most phones can't upgrade (officially) without a signed firmware package designed to upgrade from the existing version of Android that's already on the phone.  In those cases, you can't upgrade without rooting and/or unlocking your bootloader and/or flashing a custom recovery, which all void your warranty.

Some phones may not be as limited; for example, the original software on the original Galaxy S devices allowed unsigned updates to be flashed without needing to unlock the device.  Theoretically you could try to flash a firmware package from a different region; it's hard to say how that would affect your warranty (and besides, that's really off-topic here :P).  You could also of course flash a custom ROM with a newer version of Android, which again will void your warranty just like rooting.