It is only very recently that scientists figured out how to determine how old a lobster is [1], as they show so very few signs of aging. Crustaceans are a pain to work with in this respect as they shed and regenerate almost everything that might be used to easily mark age, and the behavior and capabilities of a fifty year old lobster are not noticeably different from a ten year old lobster. They do age, however, just in nowhere near the same way as mammals.

A number of lower animals seem to have indefinite life spans, but that may be because few people are willing to put in the time to figure out whether they only have very, very long life spans. Hydra, for example, are one of those cases. [2] These species are not terribly relevant to any human medicine. Hydra are (probably) long-lived because they are ferociously competent regenerators, little packages of stem cells essentially. Once you have a complex nervous system you can't run the "regenerate everything all the time" model, however, as the fine structure of your brain needs to stay the way it is.

The AnAge Database lists a few more species considered to have negligible senescence that are of more interest because they are more complex organisms. [3] Longevity figures are often a question mark here, as there is too little study to determine what life spans actually are if these animals are left alone in a place where they have food and won't get eaten or diseased.

[1]: http://www.huffingtonpost.com/2012/11/30/lobster-age_n_22159...

[2]: https://www.fightaging.org/archives/2012/11/investigating-th...

[3]: http://genomics.senescence.info/species/nonaging.php

Several. http://en.m.wikipedia.org/wiki/Biological_immortality

Maybe in a perfect environment. They haven't evolved planned death because the chances of surviving longer aren't very high. From an evolutionary perspective death enables: mutations, variety and adaptation. Without it a species will stagnate and become extinct.