I have been compiling a list of songs that are, in some way, magical for me, and looking up (as best I can) their authors, composers, & dates; so I can give a quantitative answer to this question. So far there are 280 songs on the list.

Anon. wins hands down, with 99. Runners up are Robert Burns & Rudyard Kipling, with 5 each. Stan Rogers has 4, and Cyril Tawney, Woody Guthrie, and Michael Flanders have 3 each. There are twelve who have 2, and the rest are 1-hit wonders.

The median date of composition is 1900.