In general, I don't listen to the words of a song and am reduced to tears.
'Tears in Heaven' by Eric Clapton is definitely a sad song because of its content, but it doesn't make me cry.
I do still cry when I hear certain songs, but that is mostly due to what I am going through in my life.
Gotye released 'Somebody that I used to know' not long after my ex of 18 years and I split in what I believed to be amicable (we haven't spoken since). This song killed me, and it's only been in the last year that I have been able to listen to it without tearing up.
More recently, I had to put my little fur baby down, and being a single guy with no kids she meant a lot to me, having rescued her not long after the afore mentioned split. A couple of days later I heard 'Bright Eyes' from Watership Down on the radio and just lost it.