Automatic Swimming Pool Cleaners

There are three types of automatic pool cleaners: booster-pump systems, skimmer systems, and robotic.

Automatic Pool Cleaners - Booster Pump Systems
Booster-pump systems take water that is already on its way to the pool (after going through the filter and heater) and turbo charge, or further pressurize it by running it through a separate pump or motor. This high-pressure stream of water passes through flexible hoses into a cleaner that roams the pool.
Vacuum Head Pool Cleaner
The vacuum-head cleaner has a catch bag for collecting debris. Pressurized water from the booster pump enters through the stalk (a port on the top of the cleaner). Some of the water is blasted out of the tail, stirring up dirt on the bottom so that it can be filtered by the pool's circulation system. The rest of the water powers a turbine on a horizontal shaft that turns the wheels and moves the unit forward. Some water is diverted to a thrust jet, which can be adjusted up or down to keep the unit from moving nose-up. The head float keeps the unit in an upright position.
Sample Booster Type Pool Cleaners
Hayward Viper, Polaris 280 & 380, Letro Legend 

Automatic Pool Cleaners - Skimmer Systems
Automatic pool cleaners that connect to the pool's skimmer use the suction from the skimmer to constantly vacuum the pool. A standard vacuum hose 1 inches in diameter connects the skimmer suction opening and the vacuum head that patrols the pool bottom.
The only trick to keeping a skimmer-connected automatic pool cleaner function effectively is to keep the pump strainer pot clean. As the vacuum patrols the pool, it collects leaves and other debris and sends it to the pump strainer pot. When the pot fills with waste, suction is dramatically reduced, causing the cleaner to become in-efficient. To prevent this, clean out the strainer pot or ass a leaf-collecting canister to the vacuum hose.
Sample Suction Type Pool Cleaners
Baracuda G4 & G3, Kreepy Krauly, Eliminator Zap Vac, Hayward Navigator

Automatic Pool Cleaners - Robotic
These types of cleaners run independent of your filtration system. All dirt and debris collected is stored in a bag or cartridge contained within the cleaner. They are electronic in nature and require a standard 110-volt electrical supply but a built in transformer steps the power down to a simple 24-volt device. These cleaners have been gaining tremendous popularity because they do not engage your filter system or surface skimmer and they act as a secondary filter within the pool. They seem to be slightly more expensive to buy relative to the price of other cleaner types on the market.
Sample Robotic Type Pool Cleaners
Aquabot Turbo, Aqua Jet