If we're looking for specific examples, we should probably go back through the Brikwars site's archives and find actual historical examples from past games. Truth is stranger than anything we can make up.
Example: The Mighty Benny of Deconstructionism: awarded for using the local architecture as an offensive weapon.
(Image from BLOC's Death to the Pepsi Brotherhood game)
Pieces: A PBB Hammer attached to a severed minifig hand.
Ideal use: Damage rolls in attacks against structures.
Just one random act of violence can brighten your day. Especially if it involves explosives.