There are a few songs I have learnt from oral transmission, without ever hearing a recorded version:

Who's the fool now?
Jones's ale
Ranzo
Bring us a barrel

Camus wrote about going in search of "those two or three great and simple images in whose presence [one's] heart first opened", and I'd say something similar about the songs that are really worth passing on: they're the ones that opened up folk music for you and stayed with you ever after. Nobody will have the same list; I'd include Ranzo and Jones's ale, but also Thousands or more, Come write me down, Blackwaterside, The valiant sailor...