I didn't know The Cat Carol, and have just googled the lyrics 
Ave Maria - Mum loved this and it was played at her funeral. I almost passed out from stifling what was going to be a huge roaring sob 
Any classic Dusty Springfield song as they remind me so much of Mum. But If You Go Away in particular.
Walking in the Air. It's only as an adult I cry at The Snowman. Reminds me of lost childhood innocence and the people I've lost. Hurts more at Christmas.
Last Christmas - Wham. Poor George. Was such a shock when he died.
Decades - Joy Division. Beautiful and bleak.
All Cats Are Grey - The Cure. In fact, the entire album Faith.
Live To Tell - Madonna. Reminds me of a tough time in childhood.
Tchaikovsky - Hymn of the Cherubim. I'm not religious, but this is very moving.
Gregorio Allegri - Miserere. As above.
However, Leonid Kharitinov's version of Song of the Volga Boatmen lifts me right up when I'm feeling bad.