You guys should watch Solty Rei, it had some great drama and some sad scenes that you won't forget, not as major as the mainstream anime out there, but still memorable ones.
I don't really cry, but these were real tear jerkers:
-Angel Beats
-Ano Hi Mita Hana no Namae o Bokutachi wa Mada Shiranai
-Battle Angel OVA
-Bokura ga ita
-Byousoku 5 Centimeter
-Clannad After Story
-H2O ~Footprints in the Sand~
-Grave of the fireflies
-Kimi Ga Nozomu Eien
-Ninja Scroll
-Phantom: Requiem for the Phantom
-Saber Marionette J-X
-Samurai X betrayal
-Outlaw Star (That one episode where Hanmyo makes her first and last appearance)