Short for Kareshi Kanojo no Jijou. See: His and Her Circumstances
Anno Hideaki (of Eva, Nadia, Gunbuster, etc) directed adaptation of a popular shoujo manga. Opinion on this anime is divided because of the inevitable GAINAX budget crash near the end of the series. Also, it ends oddly, possibly because they were gunning for a second season. It depends on whether you think an entire episode using paper cutouts of the characters on sticks is clever, cheap, or both. Undisputed is that it is hilariously funny. Look for the numerous Eva references in the series.
Also I'm making this entry because the wiki decides that it is a link and it gets annoying to have the red dashes.