Crossdresser

In short, this trope is about "dressing in the clothing of the opposite sex." The long version can get a little more complicated.

Crossdressers may be men dressing as women, or women dressing as men. Contrary to popular belief, crossdressing does not necessarily imply homosexuality. Sexuality being a fluid, confusing and often contradictory thing, no hard and fast rules can be drawn about crossdressers and transvestites. An element of sexual arousal ("transvestic fetishism") may be involved in dressing, but not necessarily. And sometimes the primary purpose for crossdressing is simply disguise. This supertrope covers all the various possibilities and permutations.

Distinguished from Drag Queen, which tends to be strongly associated with gay men and has an inherent aspect of "performance." Also not to be confused with transgender, which describes a people who consider themselves to be members of the "opposite" sex. There's always potential for overlap, however. A drag queen may also dress as a woman while "offstage," and thus be a crossdresser as well. Some people may start out as "merely" crossdressers, only to eventually discover that they are transgender.

"Crossdresser" and "Transvestite" aren't necessarily synonymous in Real Life. Many different (and often contradictory) definitions for each term can be found. This trope is intended to encompass all of them—at least for purposes of troping.

Note that, since the 1960s or so in western culture, there tends to be little or no social stigma attached to women wearing "traditionally male" clothing. Once upon a time, however, a woman dressing like a man (e.g., wearing trousers) would be frowned upon, or even illegal in some jurisdictions - this was one of the crimes that the English charged Joan of Arc with after they captured her.

Tropes about characters and their clothing choices:
 * Wholesome Crossdresser: Crossdressing characters (of either sex) presented in a positive (or at least neutral) way. Often presented as physically attractive.
 * Creepy Crossdresser: Crossdressing characters (nearly always men) played for weirdness, creepiness, Squick value, or to show that a character is evil or deranged.

Tropes about dressing as disguise:
 * Disguised in Drag: Men disguise themselves as women.
 * Sweet Polly Oliver: Women disguise themselves as men. See Samus Is a Girl for the reveal.
 * Recursive Crossdressing: Women disguise themselves as men disguised as women, vice versa, or any permutations thereof.

Tropes about other character's responses:
 * Dragged Into Drag: Girls love helping boys dress as girls.
 * Sweet on Polly Oliver: Straight guys find another guy disturbingly attractive... because "he" is actually a girl.
 * Attractive Bent Gender: Men dressing as (or transformed into) women become hot women.
 * Unsettling Gender Reveal: The confusion caused by the person a character was crushing on turning out to be the opposite gender of what they assumed.

See Also Ambiguous Gender, Viewer Gender Confusion, Bifauxnen, and Dude Looks Like a Lady, tropes which share some common aspects with the above but generally are not about deliberate crossdressing. Like Drag Queen, Crosscast Role involves crossdressing, but only in the context of an actor playing a part.

Live-Action TV

 * Parodied on Little Britain, which featured Emily and Florence, who would dress and attempt to act like 19th century women and insisted that they were lay-dees. Florence has a mustache.
 * Mr Richard McCourt dancing the tango in a very fetching dress on Dick and Dom in da Bungalow
 * British television has a proud tradition of men dressing as women for comedy. It probably goes back to how men (or boys) played female roles in Shakespeare's day.
 * Monty Python's Flying Circus did this in every episode. It probably helped that the troupe didn't have any women (or just one woman, Carol Cleveland), so at least some of the crossdressing was actually necessary. It mostly served to make the character appear middle-aged and frumpy.
 * Benny Hill did it regularly.
 * A Bit of Fry and Laurie did this all the time, too.
 * Noah's Arc: Romeo borders between this and a very effeminate man.
 * Boy Meets World reveals that main character Shawn Hunter is a wannabe crossdresser. In Chick Like Me s4e13, he tries to convince Cory to crossdress for an article about how differently boys and girls are treated. When he tries coaching Cory, Topanga realizes that Shawn is much better at it, convincing him to do the actual crossdressing, instead. He then admits to having thought about it before. By the time they go to college, he's been a public crossdresser (of-screen) so long that other characters turn to him for advice when they crossdress in What A Drag.

Manhua

 * Xiao Meng the eunuch assassin from Chinese Manhua Ravages of Time insists he's a man, but specializes in disguising himself as a woman.

Theatre

 * Common on the Vaudeville circuit.