A popular subset of cosplay which involves people cosplaying characters of the opposite gender, or "gender-bending" those characters.
"Crossplay" is the catchall term used in the west to refer to any cosplay that involves gender-bending. Its most common forms are:
Cosplaying a character that is of the opposite gender
Wearing a style of clothing associated with the other gender (but not a specific character, e.g. a male maid)
Redesigning a character to match one's gender or "gender-bending" a character (e.g. female Kyon, female Vash, etc.)
These are the most common usages, although some do not think of the latter as true "crossplay" since it usually results in people cosplaying their own gender (even if the character was originally the opposite). Women cosplaying as male characters is also extremely common, and there are some who don't consider it to be really "crossplay" either.
Perhaps the most famous of all crossplayers is ManFaye, a man who cosplays as Faye Valentine from Cowboy Bebop at Anime Expo. Originally a rather chunky and extremely hairy man, it was considered funny by many (and disgusting by some) due to the shortness of Faye's shorts. ManFaye has actually been evicted from the convention at least once, because he was wearing a thong. (Of late it appears that he only dresses as ManFaye outside the convention facility, and wears street clothes inside.)
There have been a number of ManFaye-inspired costumes, including several Man Yunas, Man Chiis, etc.