For questions generally related to bicycle sports, including road racing (sprint and long-distance), velodrome, mountain cycling/cyclocross, BMX and stunt bicycling. Also related to combination events such as triathlons. Another place for questions about this topic might be bicycles.SE site, in particular (racing) tag.
A bicycle is a two-wheeled, human pedal-powered vehicle, commonly used for everyday transportation especially in urban areas. As a sport, bicycles are commonly raced on and off-road, with several forms of stunt cycling recently becoming popular as "extreme sports" featured in the Summer X Games.
Road bicycling is contested on paved outdoor courses many miles long, divided into sprint and endurance races, and racers typically use a lightweight medium- to large-frame bicycle with large-diameter, narrow-rimmed wheels with grooved or slick tires, narrow handlebars with a downward curve allowing a more tucked rider position, and multiple gears for varying slopes and speeds. The most famous endurance race is the multi-stage Tour de France, in which competing teams of cyclists, each with a star "anchor" cyclist and several "support" riders, race in various courses called "stages" located around France, from Paris to the Pyrenees Mountains, including both sprints (time trials) and longer endurance races (some of them up to 200 miles in a single stage)
Velodrome bicycling is a form of sprint cycling done indoors on a special banked oval track called the velodrome. The bicycle used is specialized, mostly similar to a road cycle, but with no brakes and only one gear, and optimized for aerodynamics over extreme light weight, with teardrop tube shaping and aerodynamic "shells" over the spokes of the wheels. An event can be between 1km and 30km depending on the exact race, and can be either an individual event with contestants racing in pairs or as heats of up to 9 racers, or a team event with two or more teams of three, four or five cyclists each taking turns "drafting" behind each other, usually in much longer events.
BMX or "bicycle motocross" is performed on a bare dirt track similar to its parent sport of motocross, which uses a motorcycle. The course is typically artificially constructed with hills, bumps, ramps and banked curves, and is often enclosed in a stadium for spectator events. The bicycle used has a sturdy small to medium frame, strong wheels with knobby off-road tires, and usually a single gear. Racers compete in heats of up to a dozen cyclists at once, and the events are usually simple distance races; the first to complete one or two laps of the course wins.
Mountain cycling is an off-road form of cycling most commonly undertaken for recreation, but also used for racing. The venue is typically a trail or other path through natural terrain up to and including steep rocky slopes, though sometimes a dirt track similar to BMX is used for sprint races. A common variant is "downhill cycling" in which a course on a long slope is artificially created with ramps, and rises. A mountain bike is typically a medium-framed cycle with sturdy large-diameter tubing, often with shock absorbers in the front or rear, straight handlebars allowing high leverage, wide-rimmed wheels with wide knobby tires, and multiple gears. Larger variants without shock absorbers and/or less pronounced tire tread are known as "trail bikes" and are suitable for general recreational use on paved or gravel roads and trails, but not the more advanced mountain climbing.
Cyclocross is a hybrid of road and mountain biking, using a bicycle similar in general appearance to a road bike but smaller and with off-road tires. Racers compete in heats around a relatively short course - 1 to 2 miles - with terrain ranging from paved asphalt to concrete to grass and bare dirt. It is unique among cycling formats in that many situations require the rider to dismount, pick up and carry their bike across an obstacle such as a steep incline or over hurdles, before setting down and re-mounting their bike for the next portion.
Stunt biking is a variant born from BMX racing, in which the focus is on the skill and creativity of the rider in performing tricks, instead of speed and agility around a track. The bicycle typically used depends on the exact event but is usually similar in form and construction to a BMX bike, often with the addition of extensions to the two axles called "pegs" that the rider can stand on, and in smaller or larger frame and wheel sizes depending on rider preference and the exact format. Formats are similar to those used for skateboarding or dirt bike stunts, including the "vert ramp" (half-pipe), "flatland" (no ramps or obstacles), "park" (varying from a "flatland" course with added wooden ramps up to hybrids of a "vert ramp" imitating a dry swimming pool) and "street" (using the "flatland" course with added ramps, rises, stairs, handrails and other "everyday" obstacles), as well as "dirt jump" (similar in theory to ski jumping, a long downhill run-up to a large dirt ramp allows riders to have very long "hang times" for extreme flips and other tricks) and "dirt park" (similar to the "park" format but with a dirt surface instead of concrete and wood).