Rallying[[note]]This page refers to the motorsport of rallying, rather than other uses of the word rallying that may appear in the English language, a list of which can be found [[http://en.wikipedia.org/wiki/Rally here]][[/note]] is a motorsport in which drivers and co-drivers compete against the clock to be the fastest from point A to point B. By 'against the clock' we mean that each car is sent out at spaced intervals; you're not going to see a NASCAR-style Big One.
Courses are practically never purpose built. Instead, they're laid out along normal roads closed to traffic. Note that these need not be ''paved''. Or dry. Asphalt, dirt, gravel, rain, snow, whatever. This leads to one of the more popular images, a rally car exiting the intended route -- and depending on drainage ditches, roadside obstructions, and the mood of the racing gods, landing on a side other than the one with wheels. This goes back to the roots of rallying, which are around the roots of the automobile itself--after all, no-one was building superspeedways or elaborate road course tracks in 1890.
The co-driver is more than just a passenger, mechanic, or a guy to help roll your car back on its wheels when you dump it in a creek. In-car video and audio will often feature the co-driver looking over a detailed set of notes and reading instructions to the driver regarding what's coming up. In most professional rally events, the notes are provided by the organising staff well in advance, or even by the driver having taken a dry run along the course ... but in older or lower-division rallys, the course itself may be kept secret until the end.
The WorldRallyChampionship has done much to popularise the sport around the world, with its distinct driving style; the low-grip road surfaces encourage drifting to the point that some fans have joked about rally drivers never looking out the windshield of their cars. Fans at rally stage events can have another unique experience ... safety allowing, they can go out and aid a driver! This is usually not frowned upon, as the usual case where a fan would have any way of aiding the driver is the position of a car being 'off track' and likely 'on lid'.
The cars themselves tend to be what Americans might consider 'compact'. Ford's Escort (and later Focus), Subaru's Imprezza, and Toyota's Yaris and Corolla are things most Yanks can find around town. Other marques participate, too: watching WRC footage may be the first exposure of a North American fan to Citroen, or Seat, or Skoda.
A typical modern rally will last around 3 days and feature somewhere between 12 and 30 stages, linked by untimed sections driven on open roads at regular, legal speeds, and service stops, often held overnight and / or in the middle of the day.
'Rallycross' events are different: these are lap races, head to head, without co-driver, on often purpose-built tracks. The cars are similar, though, and many techniques are too (although blocking is something a rally driver would have to learn).