I think I remember reading somewhere that trees are technically immortal, too, because they essentially renew their internal structures every year. I mean, trees just don't die of old age (worn-out organs/internal structures), so it's always damage and diseases that kill them.
I've also heard that trees tend to live a long lifespan because they're autotrophic (create their own sustenance). Heterotrophs have to eat others to survive, and that means having to take in toxins that potentially lower lifespan bit by bit. At least, that's what my botany prof. said.