Awesome question! It could use a couple qualifiers, however...
1) How do we define organism?
2) Are we assuming the environment never changes?
CactusWoman mentioned jellyfish that continually revert to an immature stage, essentially remaining young indefinitely. We could also cite colonial organisms. For example, some scientists say the world's biggest known organism is a fungus growing over an area of many acres (in Oregon, I believe). How long could something like that live?
Then there's the environment; as Joshua said, every living thing on Earth will presumably die when the sun dies.
And there's yet another thing to consider - dormancy.
Seeds that are centuries old have been sprouted. So would it be possible for a seed or spore to survive indefinitely?
In this spirit, some have suggested that life on Earth began when the planet was "seeded" by meteorites carrying life forms. A Martian meteorite that crashed into Antarctica created a sensation when it was announced that it might contain evidence of primitive life.
Whether or not the meteorite was "inhabited" is a matter of debate, and if life evolved independently on Mars, why couldn't it do so on Earth?
Nevertheless, to truly live forever - or even for a mere 100 billion years - an organism would presumably have to somehow escape its dying home planet and float in space in a state of dormancy...something that may or may not be possible.
P.S. I just discovered that the environment has already been discussed and pronounced irrelevant to this discussion. But I think it still makes for an interesting side discussion. ;)