There are a few and it amounts to a certain type of manga, not a single one.
In my case the most prominent examples are as you've mentioned; school days, which I didn't even finish. Kimi no iru machi(something), the guy was so pathetic I was slightly disgusted and stopped reading it. Good ending, also a series with the protagonist balancing on the zenith of patheticness, I stopped reading it.
So, it's not as if tragedy mangas are all bad, it's just that some of them irritate me tremendously, is all.