Here's my list:
1: "Anything Can Happen" by composer Marcus Miller (the theme song to the 1997 basketball dramedy "The 6th Man". This song never ceases to make me cry, and it's very hard to get me to cry.)
2: "What If" by 112 (the lead singer, Marvin "Slim" Scandric, as he sings about how he has drastically messed up his relationship with his girl and voices his regrets, you can hear the increasing pain in his voice. For an R&B song, this was the most emotional one I've heard in a long time.
3: "Toy Soldiers" by Martika (great anti-drug song coming from the heart of the Drug Wars era, this came out around 1988)
4: "She's Out Of My Life" by Michael Jackson (Nuff said. Very emotional song, circa 1979.) R.I.P. Michael Joseph Jackson