Three I have memorized recently:

Timid Frieda by Jacques Brel
The Old Lamplighter
The Three Bells (the Jimmie Brown song)

I've been scanning these lists looking for tunes to add to my dulcimer repertoire, and I have found quite a few. Thanks to all who have posted.

Acorn4,if you are still around - thanks for mentioning 'Daddy, don't become a Morris dancer.' I found the lyrics, and they are really funny.