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In terms of stopping power, disk brakes are the most powerful, working well in all weather conditions and requiring little maintenance. The downside is they are heavy and expensive. You see the two types of disk brakes--hydraulic and cable pull--most often on mountain bikes, touring bikes, tandems and some cyclocross bikes.
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Cantilever brakes are powerful, inexpensive and lightweight. They are the most common brake on modern bikes.
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Offering more control and mud clearance than cantilevers, center pull or "Y" brakes are the choice of light tourers and cyclocross racers. Some require special tools and expertise to adjust.
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Almost all modern road bikes use dual pivot brakes because they are small, lightweight and aerodynamic. Though not as powerful as any of the previous brakes, dual pivots are more than strong enough to lock up most skinny road wheels.
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The precursor to the dual pivot, single-pivot brakes have one central pivot point with off-centered cable pull points. They are not very powerful or precise, and are usually seen on outdated or very cheap bikes.
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Using leg power to push internal pads against the inner hub wall, coaster brakes are cheap, reliable, easy to use and low maintenance, but they also are heavy and imprecise. Drum brakes work using the same mechanical concepts as coasters, but they are activated by cables, therefore not interfering with coasting.
