Rei-chan is Rei Ayanami from Neon Genesis Evangelion. The girls of Evangelion have numerous fans and critics.
Pictures of Rei were banned for a month after 4channers, frustrated with all the pictures of her being flooded, started to counterflood with pictures of Rei's hair on various people and objects with the now famous "BLUE HAIR = REI", "ZOMG REI" or "IT'S REI FAP FAP FAP". Eventually the flooding stopped, but the quotes and their mutations pop up from time to time.
Sometime in 2004, Reidick, a scan of a penis with blue "hair" and the caption "TEH REI" drawn in MS Paint, was created and endlessly spamposted to /b/ by Rei-Chan, with the message "She is cute, that is why she is called Rei Chan." This message has become a meme in itself.
Reidick was also floodposted to /f/ in a Flash movie, called Teh Rei.swf (see below), with the chant "Internet FUCK" in the background, which predictably got saged mercilessly as fast as it was reposted. Reidick has appeared in more legitimate Flash movies, notably "Sage Man" by Okk, and the /b/ version makes a surprise appearance in Disaster Labs' "8-Bitch Fyve: Evil on the Attack".