Like Alaska Mike, I sing my own. But an exception crept in recently, as I became besotted by the Spiers & Boden version of a gorgeous song:

"Courting too slow" (Trad lyrics, tune by Peter Bellamy)

Excluding my own, other songs that I trot out from time to time:

"Ik zeg adieu" (trad Flemish, c 1645)
"Belle qui tiends ma vie" (French madrigal)
"Come all ye worthy Christian men" (trad hymn)
"The battle of Alma" (trad)
"When you are old and grey" (Tom Lehrer)
"Girl on a train" (Pete Atkin)
"The Flowers and the Wine" (Clive James/Pete Atkin)
"Love on the sands" (Jeremy Taylor)
"Drinking with Rosie" (Richard Digance)