I know you said "new" animes, but I'm usually a sucker for nostalgia, and I tend be behind when it comes to animes, anyways (I ususally wait for the english dubs, and I wait for the series/season to end before watching anything).
Off the top of my head, 3 tragic (old) animes that no one knows about (I don't even know anyone, personally, that know about these 3 titles) and tend to get overlooked are:
-SaiKano, which is, by far, the weakest of the 3 that I'm going to list. It came out in 2002(?). It is a romantic coming of age tragedy that touches on topics such as loneliness, war, and the insignificance of human life.
-Texhnolyze, which came out in 2003. It is a cyberpunk that focus on the de-evolution of the human condition and extinction of human society in the midst of technological and philosophical evolution.
-Ima Soka ni Iru Boku, which came out in 1999. It is a Sci-Fi drama, who's plot is centered around a war torn world that has quickly descended into chaos due to war. Although it's main theme is hope, it is unrelenting in it's imagery of the aftermath of rape and war. I believe that Ima Soka ni Iru Boku is one of the best anime series to ever be released. However, I cannot watch it again.