I think the key is how you are going to define immortal. Is it someone that will not die of natural causes, or someone that cannot die by any known means?
I also think there is the factor of immortal or god, I think that there has to be the definition of is it immortal, god or both.
So would Achilles be considered immortal or mortal.
I agree with the others, first you have to define immortal. Then next, if you can't destroy them, entrap them or remove them. So bind them in unbreakable chains and send them to the bottom of the ocean, or banish them to another plain of existence. (Of course they always get free eventually which gives you a whole new story to write!)
Don't know what else to add but defining immortal helps. I have immortals where they never age, but if you chop their heads off they will die, and i have one immortal where he can not die, at all.
Yeah, definitely define "immortal" first. Considering the definition of immortal is an immunity from death, it'll all depend on what their immortality means: old-age, invincibility, stuff like that. And if they're invincible and immortal well...it would be redundant to find a way to kill them.
A friend of mine once told me somthing I found really interesting. He defind immortality as "Having a body immune to wounds and disease. The spirit inside however is still very vulnerable. You'd simply have to essentially exorcise the spirit from the incorruptable body." I don't know of this ever being used. Hope it helps.