Here's a modern modification of a rule of thumb for shake-free handheld photos.
Anti-shake technology is a wonderful thing. By using floating elements in a lens or a floating camera sensor and gyroscopic stabiliztion (or faking it digitally), many modern lenses and most modern cameras have made it easier to get better image quality by reducing camera shake.
But it isn't perfect, and some less expensive lenses don't have anti-shake. That's where good hand-holding habits are important—and it's where knowledge of the "one-over-the-focal-length" rule is essential.
Simply (and as you'll soon learn, it's not so simple), the rule works like this: Under most circumstances, when handholding a camera, the slowest shutter speed you choose should be higher than the focal length of the lens you're using.
So, if you're shooting at 100mm, the shutter speed should be the next speed setting up, which is most likely 1/125 sec. If shooting with a 50mm, the speed would be 1/60 sec, a 28mm lens would be 1/30 sec, a 200mm lens would mean a 1/250 sec, etc. This calculation assumes that you are hand-holding the camera properly to minimize shake.
Nice and sharp: Shot handheld with a Canon 7D and Sigma 18-50mm f/2.8 lens zoomed to 50mm, following the "one-over-the-focal-length" rule with the shutter speed at 1/60 sec. Even in a large print, the image is shake-free.
Fuzzy dog: Shot handheld with the same lens at 1/15 second, overall blurriness resulted from camera shake. I can hold a camera steady, but at 1/15 second, not that steady! (I also shot at 1/30 sec and although the image was blurry it would be hard to show at screen resolution; in even a 4x6-inch print, however, it would be noticeable.)
There are other variables, from whether you're shooting without a finder (halve your shutter speed—shoot at 1/250 sec instead of 1/125 sec) to how much coffee you've had to drink. Many years ago, I was involved in a test to see if coffee intake affected a photographer's hand-holding abilities. The result? The more coffee (or energy drink) our test subjects (myself included) consumed, the more jittery you become, resulting in more camera movement.
Another factor is camera design. Most modern compact cameras (including interchangeable-lens compacts) lack a viewfinder. This forces you to hold the camera away from your body, which can result in more shaky photos because holding a camera against your face so you can compose in an eye-level viewfinder creates a natural support. So...no eye-level viewfinder? Cut the slowest usable shutter speed in half (1/125 sec instead of 1/60 sec for a 50mm lens, for example). If you have a touch-screen operated shutter release (common on camera phones), you should also assume low-light shots will be shaky. (Since you may not have any control over exposure with such cameras, you can't really follow the "one-over-the-focal-length" rule).
How does anti-shake technology help? Manufacturers may claim anywhere from a 2-4 stop improvement in camera steadiness (translation: you can hold a camera steady at 1/60 sec, a 2-stop improvement means you should be able to hold it steady at 1/15 sec, a 3 stop improvemnt would mean 1/8 sec, and a 4-stop improvement would mean 1/4 sec.) Some of these estimates may be more realistic than others; the slower the shutter speed, the less likely these claims will hold up. Caffeine-fueled jitters can also reduce anti-shake's effectiveness.
Same 18-50mm lens as above, same 1/15 second exposure, but it is sharper because I turned on the lens's shake reduction. If I had used a lens that lacked shake reduction, I wouldn't get away with such a slow speed.
If you are in a situation where there's so little light you can't get the one-over-the-focal length speed (or the one-over-the-focal-length plus shake reduction), try boosting your ISO until you get a faster shutter speed that would yield a good exposure. Otherwise, if you can't find something to support your camera, you might as well put it away until the light gets better.