One of the first times I cried from watching an anime was after watching Gundam 0080. At the time I couldn't believe that it ended the way that it did. For only six episodes, its hard to believe that was it. Regardless, I cried. Alot.
Since then, the floodgates turn on without my consent. I've cried watching alot of shows. That's why I don't like watching anime with friends. If a sad scene happens unexpectedly, its over for me. Can't let that happen. I have a reputation to uphold.
I'm gonna go for the obvious and say Clannad After Story. While I can point out flaws in the series (all girls not named Nagisa get thrown under the bus once their arc is over and are almost never seen again) that doesn't change the fact that After Story can wring tears from a boulder. Expecially episodes 16 (White Darkness) and 21 (The End Of The World). Those are probably the only episodes of ANY Anime that had me not only shed a tear, but actually full on cry.
Kanon was also pretty damn sad. Expecially concerning the Mai/Sayuri's arc and the final Ayu arc, concerning what she turned out to be. (And even though Shiori is my favorite Kanon girl, her arc made me less sad, because it made me so increadibly angry at her sister, Kaori. It did still make me sad though).
Byousoku 5 Centimeter on the other hand, not only made me sad, it is the only Anime, movie or not, that made me depressed for a while after watching it. Because the theme of distance, It made me feel like I was going to loose all my friends and those who are close to me. And that made me very depressed after the first time I watched it.
...damn, i will admit that i cried while watching an anime... when ash protected pikachu from the spearrow and pikachu finally made friends with ash... that was the greatest momment in my entire life... it still hits my heart *cry*....
Grave of the Fireflies, but I think everyone has shed a few tears at that one. And FMA,
Spoiler:
when Maes Hughes dies (probably not spoiler anymore but eh, some people may not've seen it yet.)
Spoiler:
...i will spoil too... it was very saddening... especially when his daughter was crying "daddy still has work to do"(maybe not exactly what she said) when they were burrying him...