Kinda late to the party as usual -_-;, but anyways:
1.) Clannad, both the anime and the visual novel (which I am currently re-playing on the Switch)
Anime:
Visual Novel: Kotomi's route and Fuuko's route are two of my personal favorite routes due to the amount of feels in both of them. Specifically, the scene in Kotomi's route when she receives the teddy bear from her late parents, and in Fuuko's, when she is finally able to pass on her well wishes to Kouko at the latter's wedding were both very emotional scenes that I enjoy greatly.
2.) Dragon Quest IV: Chapters of the Chosen
Rose, an elf girl that cries Ruby tears basically died due to human greed. Fortunately, in the DS port of the game (and probably other remakes) Square Enix added a post story where you can reverse this death iirc.
3.) -Crisis Core- Final Fantasy VII
I saw it coming, as I had seen Advent Children before beating this, but that ending still really hit me hard.
4.) Corpse Party: Blood Covered
I know what you're thinking "But Mika,
that is a horror game."
The (true) ending, and a bad ending from the last chapter are fairly emotional.
-Edit-
*Honorable Mentions (WIP)*
Air (VN)
The ending was kinda sad, but the game just didn't really feel fleshed-out as well as Clannad. Haven't seen the main anime yet, but I did see the ~90 minute movie adaptation.
Kanon (VN)
The original Anime (haven't seen the remake ...yet) doesn't make the list. Mai's and Makoto's routes were the two most emotional, behind Ayu's route.
Orange (Anime)
It has been ages since I saw this anime (probably close to 2 years), but it was pretty good. The live action movie adaptation wasn't nearly as good, but still fairly emotional.
TL;DR: A group of teens, through the Power of friendship + weird time-travel shenanigans help save a depressed classmate and friend from committing suicide
I'm sure there are way more that I've seen, but I can't immediately think of any.