It can be romantic or sci fi... like death parade!
Most Helpful Guy
Clannad contains death and depression, I don't think it's the kind of thing you're looking for, but it's worth watching regardless.
Code Geass also involves suicide later in the series, Black Lagoon features numerous traumatised characters and suicides (and lots of killing) but neither series really "deals" with those concepts. Neon Genesis Evangelion also features characters with various mental traumas and depression.4