The most annoying character I ever encountered was in a Champions game, built by my friend Mark purely to break the game (I suspect).
The character's name was Nexus. He had only two powers: Duplication (12 duplicates) and a Speed of 12 (out of a maximum of 12). This in a game where a SPD of 6 was pretty damn good.
What this meant, effectively, was that in any given combat Turn, once he'd spent his first action on splitting into his duplicates, Nexus (Mark) got 144 actions. The rest of us got 4 or 5 or 6 or 7. That meant that for 95% of the game, we were lying around twiddling our thumbs while Nexus scampered around doing EVERYTHING. It also meant that a Turn took a long, long time to resolve.
Then, due to everyone ignoring my inspired tactical genius, my blind acrobatic Daredevilesque character ended up fighting a ten-armed octopus villain and getting entangled, while Nexus took on the villain I should have been fighting, the one with the mega-flash attack which blinded all his duplicates at once.
Not that I'm bitter or anything.