I actually explained most of this one in the previous post, but to further expound I chose to use the White House as the background since it is the symbol of America's power. Also, (cue up some NBC music) did you know that using the White House to symbolize the Executive Branch is an example of a figure of speech known as metonymy?
This is the card Blind Seer from Magic: The Gathering. He's not that powerful of a card, although he was very useful during Invasion Limited. He's secretly Urza in disguise. I use this icon when I make some sort of prediction, like the prophet Tiresias from Oedipus Rex.
One day I challenged some people to make some "D2" LJ icons and I got two nice ones. Ironically, both of the people who made those icons are no longer LJ friends with me, but I figure there's no reason to delete good work just because of some LJ drama (I was a much more acrimonious person in my younger LJ days). I use this one intermittently with my other D2 icons when I have no particular icon for a post and don't want to use my default.
I made a set of avatars from the character creator of Gaia Online. I thought of Angels/Demons, or Angemons as I call them (I probably got it from a game, I can't remember which one at the current time). This one is the "benevolent dictator" icon, and it's often used when I need to lay some smack down on my own journal. Oh, I haven't written any contentious posts yet but it'll come soon enough.