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To understand the prevalence of the ii-V-I in jazz, there are three good places to look: ragtime, Tin Pan Alley, and blues.
Ragtime was characterized by something called the "Ragtime Progression":
| (V7/V/V/V) | V7/V/V | V7/V | V7 | I |
or more simply:
| III7 | VI7 | II7 | V7 | I |
In the key of C major, this progression is:
| E7 | A7 | D7 | G7 | C |