I don't think actual songs move me to tears. It depends on how the actor/actress is performing them.
Sierra Boggess - "Wishing You Were Somehow Here Again"
Hugh Panaro - Pretty much anytime he's on stage as the Phantom
Sophia Gennusa - "Naughty"
I got misty eyed several times during Once and when I saw Donna Vivino as Elphaba.
I don't cry, but I always get shivers during "I'm Here" from Matilda. The "He smashed the door open!" and "An almighty rage grew in his great heart!" lines always get me.
I cried 3x during The Bridges of Madison County.
I'm not going to lie... I loved Ashley Brown's portrayal of Mary Poppins and I cried when she flew over the audience.
"The city seen from the Queensboro Bridge is always the city seen for the first time, in its first wild promise of all the mystery and the beauty in the world." - F. Scott Fitzgerald, The Great Gatsby