That's saying something because there are a LOT of annoying characters in anime. Nearly every series has one annoyingly hyperactive and grating idiot. In Ouran it is Renge Houshakuji (self-proclaimed manager and ubiquitous crazy fangirl)--every time she comes on screen I get annoyed. In Bleach there are a ton of annoying characters...too many to list. In Yami No Matsui those effing bird librarians have such horrifyingly irritating voices and personalities that they should be eaten by dragons out of principle.
But Haruko Haruhara wins, not just because she's annoying, irrational, stupid and ultraviolent, but because I find the entirety of FLCL annoying. It's just so...dumb (for the lack of a better word). Just DUMB! And because she is the most annoying character on the most annoying anime she has earned Day Six props.
Congrats! You are annoying!