At a concert, or other location when the subject is far away from you (and out of your flash range). In these cases, turn OFF your flash and hold the camera super steady, especially if it is dim lighting.
When the subject is very close to you, and using a flash will either injure the subject or wash out your picture.
In a low light situation when you want the background to be well lit. If you use the flash, your subject will be lit, but the background dark. Again, use a tripod or lean the camera on something to keep steady. When there is low light, your lens has to stay open longer to capture enough light for the image, leaving more opportunity for motion to blur the pic.
***If you are photographing a subject with a dim background behind, many cameras have a mode called "slow-sinc flash". Use it. This keeps the lens open to capture the background, but lets off a flash too to light up your subject in the foreground.
When you want to make creative use of the available light. I love to take pictures of my kids staring out windows for example, and leaving the flash off just adds a "mood" to the photo that you can't capture with the flash on. I love capturing flowers too, and a flash can flatten the beauty. Maybe you want a creative silhouette... go crazy!
Photography is art. Play around with the flash on and the flash off to see what effects you get. As I said before, take lots and don't delete your pictures until you download them. A large memory stick is a great investment!
Have fun, and post those pics for me to see.... I've heard from some of you that you are gathering up your best shots for the contest! Can't wait!
Coming soon... how else to minimize blurry photos, and how to avoid glare on glasses.