I am a big Anime Lover and it just makes sense that the saddest scene I probably have watched  was Going Merry's Funeral (One Piece).

Going Merry was the name of the Straw Hat Pirates first ship and was with them from Episode 17 to Episode 312. That's 295 Episodes right there. I still honestly don't know what happened but it just made me teary-eyed to see them saying their goodbyes to this inanimate character in the series. Probably after watching One Piece over and over again (at least 3 times prior to that scene) I somehow got attached to all of them, including their ship.

A close second and probably the first ever scene that made me cry (or at least teary-eyed) was Butterfree leaving Ash because of damn Love!. It literally broke my heart to see Ash's first ever caught pokemon in the wild leave him for some pokemon he just met.