I wanna cry

a short movie but very nice, funny and sad: Hotarubi no Mori e

https://myanimelist.net/anime/101/Air
https://myanimelist.net/anime/6547/Angel_Beats
https://myanimelist.net/anime/877/Nana
https://myanimelist.net/anime/32729/Orange
https://myanimelist.net/anime/529/Saishuu_Heiki_Kanojo
https://myanimelist.net/anime/23273/Shigatsu_wa_Kimi_no_Uso

From me I guess.

A series, but still: Fruits Basket is quite sad, but also funny

I really liked the melancholic style of 'Wolf's Rain'.

Byousoku 5cm

Angel Beats! is a series, but it's only one season. It's got a lot of action, much comedy, and the waterworks really get turned on toward the end of the series. It will make you cry, but without leaving you depressed. Angel Beats! also happens to be on Netflix at this time, if you don't do CrunchyRoll.

Boku no Pico

I think a lot of anime listed by others aren't really sad. A lot of them are really good anime with dramatic elements, maybe a sad moment here and there. but I wouldn't count them as overall sad.
Of course, if you're not actually picky about how sad it is and just want to watch good anime, there's no problem.

(I think Grave of the Fireflies is hard to beat for top of the list. It was so depressing I couldn't even finish it T.T)

I don't think you wanna keep this behavior after Grave of the Fireflies. :)

Nobody mentioned my favourite anime yet, but it was the reason I started watching other romantic/drama/sad animes.

Plastic memories

Dokuro-chan is a short series that has a few really sad moments..

Not sure if it's been mentioned already, but Wolf Children and The Wind Rises.