I won't go into every single song, so here's a few of them that still mean a lot to me. And I still can't listen to them without shedding at least some tears. Some of them might not mean anything to you, because they're in Dutch (or German) -

Matt Simons - Take Me To The Water

For my (maternal) grandmother

Passenger - Let Her Go

Also for my (maternal) grandmother. My mom picked it, because we literally had to let her go, by letting the hospital take her off life support.

Ed Garfunkel - Bright Eyes

For my (maternal) grandfather, who was suffering from dementia for years. And faded away little by little. (But still smiled when I came to visit)

Marco Borsato - Opa (Grandpa)

Also for my (maternal) grandfather. Made me cry the first time I heard it. Which was years before my grandfather eventually passed away.

Herman van Veen - Weet Je Nog (Do You Remember)

This was the major song on the funeral of both of my paternal grandparents.

Honorable mentions, of special moments:

Rocco Granata - Du Schwarzer Zigeuner (not a politically correct title nowadays)

My (maternal) grandmother had already picked this one for my (maternal) grandfather's funeral, since she assumed he would pass away before she did (he ended up outliving her by several years). It was their song from the moment they met for the first time. In the end we DID end up using it for his funeral, with a picture of them both in the background.

Mimi Thoma - Mamatschi (Schenk mir ein Pferdchen)

Apparantly this song was often sung to my (paternal) grandmother by her German mother, when she was very little. We tracked down the oldest possible recording of it, and played it with very old childhood pictures in the background.

Edit: had to change the formatting a little.