What is the biblical basis for the eternal existence of the lost in hell?

I've heard particular denominations claim that although hell is definitely a real place and hell itself will burn forever, people who are condemned to hell don't actually exist forever in hell but instead are eventually destroyed, wiped out of existence. They claim that the soul being naturally immortal is a pagan idea, and that only those given eternal life will live forever. As far as I know most mainline denominations affirm that if you are not saved then you will indeed exist forever in Hell. My question is, what is the biblical basis to support the doctrine that people who are condemned to hell will actually continue to exist in hell for eternity (as opposed to being annihilated)? Alternatively, what is the biblical support for the soul itself being naturally immortal?