Here are stories in which somebody (usually Harry) engages in the act of self injury (cutting, burning, etc.) or he attempts suicide.
I won't list any successful suicides because I had character death stories.
There Is Still A Hope After Hope Is Gone by Pip2 (rosworms)
Harry has a problem and Snape finds out. (complete) **SI**
But I Don't by Pip3 (rosworms)
Harry deals with his pain in an unhealthy way while somebody watches over him. (complete) **SI**
A Year Like None Other by aspeninthesunlight
It all started with a letter from home and family. Except, Harry doesn't really have either, does he? He's about to get them. A Snape-adopts-Harry story providing an alternate 6th year. Winner: Multifaceted Best Genfic, Best Draco Fic. (complete) **SI**
A Summer Like None Other - sequel (WIP)
No Inhibitions by Wench of Hogsmead
Harry drinks a potion that strips him of all reserve. Now he and Prof. Snape must deal with the consequences. No Slash. (WIP... not updated since 2005) **SU**
Death Is A Blessing by Nation El-Diablo
Harry is rescued from the Dursleys only to find himself in danger from former friends, and hope in a new family. (complete) **SI**
The Talisman by chips challenge
Harry disappears suddenly and when he returns he has a glowing talisman embedded in his neck. Severus claims that this can be used to control him and it must be removed, but its absence causes Harry great pain. Harry, Snape, and Sirius centric fic. (complete) **SI (not a big part, but it's there)**
The Talisman II: Inside - second story (complete)
The Talisman III: Remainder - third story (complete)
The Talisman IV: Treasure - fourth story (complete)
The Talisman V: Founder's Apprentice - fifth story (complete)
more to come from that series...
USED by zorro x
Harry says he's all right. For the most part, Ron believes him. (complete) **SI**
Stronger Than Hope by Alaunatar
An obsessed, grieving Harry has decided on a dangerous way to defeat Voldemort. Snape is paying closer attention than before, but his contempt for Harry blinds him. Eventual Snape as Harry's guardian story. (complete) **SU**
Solstice by samhaincat
Harry has trouble coming to terms with Sirius' death and finds himself once again having to take occlumency with Snape. This is the beginning of their growing relationship as Snape starts to see the green eyed wizard in a different light. Snape finds himself being a father figure to both Harry and Draco as the Dark Lord's power grows. (WIP) **SI**
Well No One Was Watching by ShadowSSnape
Harry enters a low point in life, he doesn't think anything or anyone matters anymore. Sinking lower and lower, who will help Harry before it is to late. (complete) **SI/SU**
Living 101 - sequel (WIP)