Great question as ever Derek,

I don't know the answer but really doubt it.

Cancer is regularly initiated within multicellular bodies by the effect of cosmic rays - a cosmic ray passing through a cell "billiard-balls" an electron into a location where it should not be (sometimes helped along by the tunnel effect) , leading to a ionization of the cell, which in turn leads to a waterfall of consequences (owing to plus and minus charges realigning themselves and scrambling the cell) that can lead to the establishment of an initial "cancer seed".

Higher organisms, such as the human body, have built-in mechanisms that most often manage to do away with such scrambled cells, but it's hard to see how any organism could be fully immune to this. Of course, this is but one of the ways cancer seeds can appear.

Derek:

My always insightful colleague Joachim is on target: naked mole rates (NMRs) are one of the most cancer-resistant lifeforms ever studied - and resistant to both spontaneous cancer but also to experimentally induced cancer - and with the longest reported rodent lifespan, and much has been discovered about their anti-tumorigenic capabilities, part of which involves highly enhanced cell signaling via p53 and Nrf2 [1] and by a concerted necrotic cell death mechanism [2]. Nonetheless, this is high-resistance but it is known that NMRs have contracted (spontaneously) renal tubular adenomatous hyperplasia with nuclear atypia and compression [3], a preneoplastic lesion that can be inducted into true malignancy, although this is nonetheless extremely rare, so I give credit where credit is due: Long Live the NMR! We have a lot to learn from them about countering aging and cancer.

References

Although abnormal proliferations can be seen in invertebrates, I don't think that metastases or invasive tumors have been found. In that sense, one could say that cancer is rather specific for vertebrates.

Yes, Naked mole rat, but I heard that chimpanzee  did not get cancer!!

Daniel, Nasser and Others:

It's a bit more complicated than that so let me add some qualifications to hpefully enrich this discussion further:

First, although many invertebrates have non discrete organ systems and also lack open circulatory systems with large blood sinuses, nonetheless we now know based on studies of oncogenesis (carcinogenesis and tumorigenesis) in invertebrates that neither lymphatic nor blood/circulatory dissemination is requisite for the metastatic cascade, which can actually be supported across epithelial tissue alone, as shown by the pioneer work of the Shearn Group which first demonstrated that Drosophila cells can metastasize through epithelial tissue and colonize new sites distant from the initial tumor [Beaucher, Dev. Biol 2007], and since confirmed in other invertebrates. But Daniel's point as I read it is the extreme rarity of such phenomenon in invertebrates and the high preferentiality of metastatic development in vertebrates.

Second, although Nasser is right that cancers are decidedly rarer in chimpanzees than in humans, nonetheless dozens of cancers have been thoroughly documented in the chimpanzee, such as lymphomas [Binhazim, J Med Primatol. 1997], sarcomas [Fujisawa, J Med Primatol 2014], hepetocellular carcinoma [Porter, J Med Primatol 2004], GIST [Bommineni, J Med Primatol 2009], endometrial cancer [Toft, Veterinary Pathology 1975], and over two dozen other epithelial/solid tumor, hematological, and sarcoma malignancies.

I would suggest that the positive lessons to take away from these discussions is in particular, the WHY of it all: what makes the naked mole rat, most invertebrates and certain primate vastly onco-resistant, and part of the answer from hundreds of studies is a hyper-developed TSG (tumor suppressor gene) network, which I would suggest from my reading of the data, is itself protected from defeat through oncogenes by virtue of advanced epigenetic mechanisms (including some that appear to be dietary in origin) that far more aggressively than in humans silence oncogenes and activate TSGs, at a level only rarely achieved in human clinical studies although I would predict that may be changing now as we go forward, realizing the greater importance of epigenetic processes over strictly genetic ones.

Remaining still unanswered is, all in vivo cancer model were developed after different carcinogen exposure, however cancer development is very slow process, for example breast primary epithelia cells eg:76N, rarely see if any one of us able to develop a good cancer model compare to Immortal MCF10A (immortal cells), etc or after immortalizing primary cells. Etc

..

There is "standard" answer, that insects don't live long enough to get cancer.

But discovery of "Hippo" signaling pathway in Drosophila, which controls the stem cells, can be the one of the main signpost for this question.

One can consider those papers:

Laiemail et al.; Control of Cell Proliferation and Apoptosis by Mob as Tumor Suppressor, Mats; Cell 2005, Vol. 120, Iss. 5, pp. 675–685 (DOI: 10.1016/j.cell.2004.12.036)

Ohsawa et al.; Mitochondrial defect drives non-autonomous tumour progression through Hippo signalling in Drosophila; Nature 490, 547–551 (DOI: 10.1038/nature11452)

D. Pan; The Hippo Signaling Pathway in Development and Cancer; Dev Cell. Oct 19, 2010; 19(4): 491–505 (DOI: 10.1016/j.devcel.2010.09.011)

http://dx.doi.org/10.1038/nature11452

http://dx.doi.org/10.1016/j.devcel.2010.09.011

http://dx.doi.org/10.1016/j.cell.2004.12.036

It has been suggested by Tian et al. 2013 (Nature 499: 346-349) that extremely high molecular mass hyaluronic acid is the reason why naked mole rats do not get cancer.

Really a good question Derek, I am not sure about the organisms that do not get cancer, but I wonder if some invertebrates especially worms which can easily regenerate may not get a cancer. Also, I think, cancer may be more specific to higher vertebrates. 

I also though before joining RG (at the very end of December 2015) that some "organisms" do not develop cancer ... and I recently challenged the RG community ...

I received amazing help and in two months I have a complete different view on "rarety of cancers in some organisms".

Here attached are some articles that will validate some of you and invalidate other from you ... from a scientific point of view, as I was also "strongly invalidated" by my two RG mentors in this domain: Gustav Van Niekerk and Philippe Fort!

Some of you forgot to mention the elephant story ... and the tapeworm too ...

Best regards

Robert