Seymour Cohen's special interest in the spongonucleosides
One of the scientists whose curiosity was piqued by the presence of spongonucleosides in marine sponges was Seymour Cohen. In a 1963 review-style article, Cohen wrote of his interest in these "unusual nucleosides".  He notes that the arabinosyl nucleosides were only found in a single species of sponge. These sponges existed in thick slabs and grew almost buried in sand and had to be dredged from the shallow ocean waters. Since they grow under the sand, their pores are small to prevent sand particles from getting inside. Cohen theorized that "the ecological niche of this sponge determines in some major respect the origin of the unnatural nucleosides". (In other words, the unnatural nucleosides enabled the sponges to live almost buried in sand, perhaps the spongonucleo-sides fended off enemies or helped them take in nutrients.)
The arabinosyl nucleosides were found in the free state in the sponges, meaning, the spongonucleosides were not incorporated into the chains of DNA or RNA, instead they were "readily extractable by alcohol or acetone when the live sponge is plunged into these solvents." (Somehow this brings up rather gruesome images, but it's just sponges.)
Cohen reports that the 1950s saw a great growth of interest in the chemistry of the nucleic acids, including the possibilities that these compounds - or analogues of them - might possess antitumor activity. Indeed, in the late 1950s, various unnatural nucleosides were synthesized and subsequently found to be "potent inhibitors of key pathways of nucleic acid biosynthesis", in other words, they stopped the synthesis of DNA in cells. Cohen's lab studied the metabolism of synthetic D-arabinosyl nucleosides in E. Coli.  He writes:
"Among the synthetic D-arabinosyl nucleosides which have been prepared, arabinosyl cytosine appears to be one of the most interesting . . . the substance is reasonably potent against tumors such as Sarcoma 180, Ehrlich carcinoma, and L-1210 leukemia in mice."
Arabinosyl cytosine is also called spongocytidine, and we know this compound as ara C. This is not quite the first mention of ara C in the scientific literature, though: The work using ara C in L-1210 leukemia cells was done in an Upjohn research laboratory in the group of John Evans.
Using the reference cited in Cohen's paper, I dug up the original article. Evans' group synthesized ara C and tested its anti-tumor capabilities in mice that they infected with different types of cancer cells, including leukemia cells, and found that ara C killed the leukemia cells but not the mice. They were not the first group to synthesize ara C - they cite the methods of two other groups - but they did have to synthesize the compound themselves because that was the only way that they could obtain it. (Cohen states in a footnote that he obtained his ara C from "James Hunter", who is a coauthor of the Evans paper.) They mention that they tried ara C in rats and found no anti-tumor effect, but that they could not up the dose because they did not have enough of the compound.
Cohen continued to study the aranucleosides. He was quite a prolific author of scientific articles and his research was rather broad in scope. One topic of his study was the inhibition of synthetic pathways in bacteria by potential anti-infection agents. Representative papers on his studies of the effects of the aranucleosides include:
Arathymidine is lethal to cell division in E. Coli 
The effect of arauracil on DNA synthesis in E. Coli 
Inhibition of mammalian DNA polymerase by aracytidine 
The lethality of aranucleotides 
One of the papers that Cohen coauthored  is considered a Citation Classic. These are papers that are among the most cited articles ever published. Citation Classics Commentaries are one-page articles that put a human side on these papers. In the Cohen's commentary, he states "As a result of experiments in 1956 with spongothymidine and our first experiences on cancer chemotherapy, I became interested in the potentialities of the D-arabinosyl nucleosides and problems of chemotherapy in general." (To read the entire Citation Classic Commentary, follow this Citation Classics Commentaries link and go to 1980, then scroll down the page to Cohen's name; the paper is downloadable as a pdf file.)
Cohen thought that the spongo nucleosides were not only antitumor agents, but a molecular basis for aging. Section V of his paper is entitled "Off the Deep End - or a Molecular Basis for Aging." The discussion is too esoteric even for me, and I will only include one sentence for anyone whose interest is piqued: "I [Cohen] am hypothesizing, therefore, that a molecular aging at the cellular level arises from the irreversible inactivation of critical polymers by the incorporation of arabinosyl nucleotides and the more reversible inhibition of critical reactions as a result of the accumulation of these nucleotides. Even if the specific hypothesis herein proposed is incorrect, it seems reasonable to suppose that a more general form of the hypothesis is none the less correct: namely, that irreversible damage to critical polymers and the accumulation of inhibitory products are the molecular basis of cellular aging."
More on Sidney Cohen can be found on the American Philosophical Society web site.
Research by other groups
While Cohen's paper is (in my opinion) the most readable treatise on spongonucleosides from that era (1955-1970), several other research groups also studied the effects of arabinosyl nucleosides on cell growth. A search of the scientific literature using both SciFinder Scholar (available in university science libraries) and PubMed pulls up many articles related to this topic published in this time period. I did such a search and prepared a list of journal articles. The list does not pretend to be complete, however, it serves as a sampling of what was going on during that time period, including the synthesis of ara C, studies of ara C's effects on DNA synthesis and cell growth in E. Coli, mammalian cells, leukemia cell lines, and eventually the results of trials of ara C as a chemotherapy agent in humans. The first published article that I could find on the treatment of childhood ALL is a paper published in 1966 by JP Howard.  Howard's article has been cited over 70 times.
The next section shows the chemical structure of ara C. (Skip that section if you are not interested.) The second-next section introduces you to a man who had a lot to do with getting ara C into the treatment protocols for childhood ALL.