Usagi Drop.

Banana Fish if you're fine with some mature themes, and Akira if you're fine with older anime. Akira was my first anime as an adult and it hit me hard. The whole thing had a melancholy tone that I didn't expect from a cartoon.

I have an issue with "x that makes you cry." It's a hit or miss for me because if I become acutely conscious that I'm being emotionally manipulated, I disconnect and feel detached. There doesn’t seem to be a discernible pattern. Although I know eliciting emotions is intrinsic to storytelling, some works break the fourth wall for me and I'm more focused on the strings the author is trying to pull than the plot itself, while some manage to maintain the illusion despite me being aware of what the author is doing.

Haven't watched anime in a long time but I can distinctly remember crying at The Promised Neverland Season 2 because of how bad it was 💀💀💀

Golden Time 😢

Angel Beats, clannad, tokyo magnitude 8.0, sword art online, in this corner of the world

Dororo (2019)

Haibane Renmei
Cowboy Bebop
Now and Then, Here and There - Sadly, it is now hard to find. It's about war and the brutal, dystopian world it presents is painful to watch. It's been compared to Grave of the Fireflies, and I believe it would make a rock weep.

My Teen Romantic Comedy SNAFU

Clannad and Your Name for me

can't remember much tbh, but i think Angel Beats did it to me. then it's Tokyo Magnitude 8.0.
i used to not show much emotion when watching animes and those did it for me. nowadays, most emotional anime makes me cry so i don't think i'm good enough to give recommendation based on my recent ones...

Every time that Goku has pretty much lost a fight but, instead, comes back stronger makes me teary eyed. Every. Time.

Link Click - every episode is a different story and they are all very dramatic and sad;
Perfect Blue - I didn't like the style, but it's very powerful story about the girl who went nuts;
FLCL - almost every scene with Mamimi might make you sob, the bridge one is iconic;
Cat Soup - short movie about the cat which drown in a pool and then he was trying to save his sisters soul from the death.

Neon Genesis Evangelion series (1-26) has some tense moments, maybe you've seen this one already.
Why the heck do you wanna cry anyway?

Grave of the Fireflies Imdb
I challenge you to not cry on this one. :)

Tengen Toppa Gurren-Lagann

FLCL, Evangelion

Chii's sweet home. More specifically the very beginning, where she gets lost.I know ,weird choice.

An otherwise thouroughly wholesome, cute little anime about a lost cat that finds a loving home. Its ridiculusly cute and offers hours of fun and carefree laughs. But as a devoted lifelong cat-lover, her sadness and confusion at the start really "hits me in the kokoro", to use cringe weeb lingo. I did not effectively cry, but I felt the corners of my eyes watering up.
I am just too emotionally sensitive over this particular scenario.

Otherwise Clannad is a good one too. Other Key stories like Little Busters (I soooo love this one), Planetarian and Angel Beats are good stories with the potential of a little crying as well.

Maybe throw Anohana into the mix.

a few episodes of re:zero made me cry, especially episode 15

i cry every time a dog dies on tv. dont tell anyone or ill spray you with my toxic masculinity.

Oshi no Ko had me depressed for a couple weeks .

I haven't watched anime for a long time.
If you don't mind old anime, give Seirei no Moribito a try.

I always cry everytime I watch the episode 23 of Trigun

Haibane Renmei
Kannazuki no Miko
Madoka Magica

also special category which are anime based on Key stories done by Kyoani

Ima, soko ni iru boku (Now and Then, here and There)
https://www.imdb.com/title/tt0318898/reference

The best one!

A Silent Voice. Last scene is an impossible tear jerker for me