Inspired by 
this post.  A new category of medals: fails.  Medals would include ones for...
Dying on the last level of Angel of 100.   (or AAo666)
Dying to a Former Human's melee attack.
Setting a nuke while invulnerable and having the invulnerability wear off just before the nuke explodes.
Using a large med pack when at full health and still cautious status.
Having a phase device take you right next to a pack of large monsters.
Getting nearly 100% kills and missing it by one enemy.
Dying without getting a single kill.
Having regenerating armour (such as Tactical Armour) get destroyed.
Dropping an exotic item on an occupied square and having it fall into lava.
Failing to get a single kill during the duration of a berserk pack and having the berserk run out just as you're running up to an enemy.
The current Iron Skull medal could be a natural contender too.  :)
Anyone who wants to add suggestions to this list is welcome to do so.  I might add more if I think of any.  :)
EDIT:  Ooh, another one:  Dying while standing on a Supercharge or Megasphere.  (Or invulnerability or berserk pack, for that matter)  :)