This page is intended to point out the advantages of different types of bicycle brakes, and so link to separate articles on servicing them.
Also see the table of contents page covering articles about brakes.
A bicycle brake may work at the rim, or at the hub. Rim brakes have the advantages of light weight, large heat-dissipating area, low stress on the bicycle frame, fork and wheel -- though heat dissipation is limited by risk to the tire.
Hub brakes are more weatherproof, and and are not affected by rim dents or wheel true. Because heat-dissipating area is smaller than with rim brakes, these brakes run hot -- but some are designed to.
Bicycle brakes are operated by hand levers by way of cables, or sometimes hydraulic lines -- except for one type of rear hub brake, called in British English a "backpedaling brake" or "foot brake". In American English, it is called a "coaster brake", an expression which dates back to the its introduction in the late 19th century -- also allowing coasting, unlike a fixed gear.
Most cable-operated disc brakes, and direct-pull brakes (one kind of rim brake, also called V brakes) require special brake levers, mostly available for flat handlebars. About these brake levers, please see Tom Deakins's page about handlebars.
There is also a page about cables on this site. Poor brake performance often results from cable problems.
With only a couple of exceptions, every bicycle should be equipped with two brakes -- front, and rear. Any brake will fail sooner or later, and then you really need the other one!
Notable exceptions are:
fixed-gear road bicycles. These can get by with only a front brake because the rear wheel can be slowed by pushing back against the turning pedals;
track racing bicycles, brakeless fixed-gear bicycles, because these are the only traffic on the track, and abrupt stops would be hazardous;
tandems and other bicycles which carry a heavy load. These generally should have three brakes -- powerful front and rear rim brakes for stops, and a drum or disc brake capable of heavy heat dissipation to control speed on descents. See the page on tandem brakes.
Adult tricycles. (OK, not exactly bicycles.) Recumbent "tadpole" tricycles, with two wheels in the front, generally have dual handbrakes -- one on each front wheel, controlled by the hand lever on its side, allowing the brakes to help with cornering. Racing "delta" tricycles, with the two wheels in the back, often have two handbrakes, both operating on the front wheel. Tricycles may have only one rear wheel driven, and only that wheel may have a brake. For safety's sake, there should always be a brake on the front wheel.