I don't remember having a specific song, like with someone I was serious about (although when young, can't always tell when being serious...maybe seriously deluded, but hey)
Though I do recall theres a song thats sad that an ex would play and I knew we were over before we had even really begun and it hurts to hear it.
Though a lot of songs pull on your heartstrings because that is what they are designed to do. If people did not sing or write poetry about their emotions, how else would they process them?
I'm more like, the songs that really affect me are when someone has died, or gone far away, or maybe torch songs for a lost love (very common)
Nothing compares to you by Sinead O'Conner comes to mind. the 'you' could be anyone you felt something with and then lost. She was crying in the video, shaved her hair off...it's very much about grieving that loss.
To listen to that or attempt to sing it can be cathartic. There are now lots of songs that I'm recalling now I've discovered spotify, but on you tube you can also bring up any song, and it will have the lyrics, even karaoke versions. I enjoy music anyway and don't mind a few sad songs, as long as I still keep the happy ones to cheer me up.
Anyway, if anyone wants to share playlists, that's fine, but its very personal what people like in their list I think. I'm very broad/catholic in music taste though. If I like something, I like it. Break up songs are universal. EVERYONE has gone or will go through a loss or departure of a loved one at some point in their lives.
If your sentiment is 'I will always love you' thats legitimate. Nothing will break the bond that you had if it was strong and you were once close.