My father loved music & we played albums all the time in our home. So any songs by Nat King Cole, Jim Reeves, Dean Martin, Glen Campbell, etc makes me cry if I'm in the right mood. Its not so much the songs as the memories around them.
"Somewhere Over the Rainbow" by Israel Kamakawiso'ole:
The story behind this is that I loved this version of the song - it had been used on some commercial years ago. Then...this was playing during the scene on ER when Mark Greene died. The episode aired a few months after my ex-husband left - I sat and sobbed.
I looked up the song and bought the CD - I love it and now have it on my iPhone. Just listened to it, and even almost 8 years later, and being happily re-married for almost 5, it still brings me to tears.
Remember When It Rained by Josh Groban (For whatever reason, this song gets me sobbing like a little baby everytime)
That's The Way by Eli Young Band (reminds me of a breakup with a particularly nasty ex)