Back to the Future (film)/Tear Jerker

The Films

Have a couple of tissues ready in Part II when Marty finds George-A's grave…
- No! This can't be happening!
The scene when Marty receives the letter from Doc can cause some to get misty eyed, the music doesn't help either. It's not sad, it more or less causes tears of joy.
Big one in Part III when the DeLorean gets destroyed. Seeing one of the most iconic props in cinema wrecked like that is heartbreaking. The worst part is seeing the flux capacitor and the time interface go out.

Marty: Well, Doc, it's destroyed…just like you wanted.

A deleted scene in Part III shows Marshall Strickland gunned down by Mad Dog Tannen, right in front of his son. He dies on the spot. It was actually for this reason the scene was taken out, though the event has been confirmed as canon, thanks to the game.
Any scene with Doc and Clara within thirty feet of each other that is not a Crowning Moment of Heartwarming is bound to be a Crowning Moment of Heartbreaking. Case in point: Right before Clara slams the door in Doc's face, she demands to know why he would make up such an elaborate lie about traveling to the future when a simple "I don't love you" would suffice. She slams the door... and cue Doc's big brown puppy-dog eyes filled with pain when he says to the shut door, "That wouldn't be the truth!"
In the second movie, there's a scene when Jennifer finds out that Marty had a car crash thirty years ago, from racing Needles when he called him a chicken. This crash broke Marty's hand, which left him unable to play guitar very well, and forever crushing his Rock Star dream. Then we see Future!Marty silently playing his guitar.
Both times that Doc gets shot. Marty's reaction might be a little Narmy to some, but...imagine seeing your best friend killed in cold blood, twice, and not being able to do a thing about it in either case.

Marty: NO! BASTARDS!