Almost all digital cameras, from top-of-the-line advanced cameras to cheap point-and-shoots—and even some smart phones—include what's called "burst mode": It allows you to shoot a sequence of photos in rapid-fire succession.
Although burst mode is obviously helpful in capturing action shots—say, at a baseball game—it has other uses: For example, when you're taking photos of babies and toddlers, burst mode can help you capture the right moment, since such subjects can be unpredictable.
In the past couple of years, both basic and advanced cameras have dramatically increased both the speed and length of the burst for full-resolution photos. Many models can fire off bursts as rapidly as 10 frames per second, and many cameras let you fire the burst for a longer length of time. Some cameras fire off for 5 to 10 seconds. Others, particularly SLRs, shoot until the entire memory card is full. Just be aware that certain factors, including low light and use of certain manual settings, may shorten the length or slow the pace of shooting in burst mode.
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Certain more sophisticated cameras combine burst mode with other features. For example, some Canon PowerShot cameras have something called Continuous Shooting AF, which not only shoots photos in rapid succession but also tracks and focuses on the subject, so that it remains in sharp focus throughout the entire burst.
One thing you'll want to note: On some devices, you may not realize that you'll be taking lower-resolution photos when you activate burst mode. For instance, if you're using a 12-megapixel camera, the model may only shoot 6- or 3-megapixel stills in burst mode. Check your user manual to find out.