Cabaret -- Madrid's nightlife is no longer steeped in prudishness, as it was (at least officially) during the Franco era. You can now see glossy cabaret acts and shows with lots of nudity.
Cave Crawling -- To capture a peculiar Madrid joie de vivre of the 18th century, visit some mesones and cuevas, many found in the barrios bajos, the area south of Plaza Mayor. From Plaza Mayor, walk down the Arco de Cuchilleros until you find a gypsylike cave that fits your fancy. Young people love to meet in the taverns and caves of Old Madrid for communal drinking and songfests. The sangria flows freely, the atmosphere is charged, and the room is usually packed; the sounds of guitars waft into the night air. Sometimes you'll see a strolling band of singing students going from bar to bar, colorfully attired, with ribbons fluttering from their outfits.
Summer Terrazas -- At the first blush of spring weather, Madrileños rush outdoors to drink, talk, and sit at a string of open-air cafes, called terrazas, throughout the city. The best and most expensive ones are along Paseo de la Castellana between the Plaza de la Cibeles and the Plaza Emilio Castelar, but there are dozens more throughout the city.
You can wander up and down the boulevard, selecting one that appeals to you; if you get bored, you can go on later to another one. Sometimes these terrazas are called chirinquitos. You'll find them along other paseos, the Recoletos and the Prado, both fashionable areas but not as hip as the Castellana. For old traditional atmosphere, the terraces at the Plaza Mayor win out. The Plaza Santa Ana has several atmospheric choices within the old city. Friday and Saturday are the most popular nights for drinking; many locals sit here all night.
Dance Clubs -- The Spanish dance club takes its inspiration from those of other Western capitals. In Madrid most clubs are open from around 6 to 9pm, later reopening around 11pm. They generally start rocking at midnight or thereabouts.