There are two characters I've thought up that I never got to play. One, because the group I was playing with fell apart, and the second because it's a little goofy for most games of D&D. Both of them were for D&D 4E.
The first character was a warforged paladin of the Raven Queen. I loved the idea of an essentially-immortal construct becoming a champion of the goddess of death. He absolutely loathed undead, because they were even stranger than the normal fleshbags he hung out with (AKA the rest of the adventuring party), and because they upset the normal balance of things. He figured that, as a warforged, he was the perfect weapon to fight undead for his deity. He was essentially the opposite of intelligent undead like vampires or liches: he would never die naturally, he was a champion for the living, and he sent undead to his goddess for judgment.
The second character, the goofier one, was a warforged bard based on heavy metal music. His theme song was Black Sabbath's “Iron Man,” and when he wasn't playing a badass guitar solo, he was using that guitar as a battle axe (it was a unique combo axe/guitar). Fun to think about, even more fun to make playlists for, but it's a character that I think would only really work for a one-shot game.
I'm amazed I was able to actually find an image of a warforged bard using a battle axe guitar. That's so awesome.