There are two things that can ruin photos - blur and being out of focus. At times, though, blur can make a picture better. The trick to doing that is understanding how to use blur as a creative tool.
The most common time to try creative blur is when you don't have enough light to get the picture you want. That often means early or late in the day, or indoors. I recently led a photo workshop in Egypt, as part of the American Photo/Pop Photo Mentor Series, and as part of that we spent three days cruising the Nile. After sunset there was still beautiful light on the water, but much too dark to get a good shot without either a lot of noise (high ISO) or blur. I told the folks out on deck with me that this was a great time to start doing some creative blur. There were water taxis running back and forth across the river, and they made great subjects for a pan shot. Panning is when you shoot a slow shutter peed while tracking your subject. You try to keep them in the same spot in your viewfinder, and the movement of your lens tracking them creates motion blur in the background. With a little luck you get a part of the subject sharp, while the rest of the scene shows blur. The slower you shoot, the greater the effect. The downside is the slower you shoot, the more likely it won't work. My answer to that is, shoot a lot! This photo of the boat was made at 1/8 second, f/13 at 200 ISO. Obviously I could have used a higher shutter speed (with a wider aperture), but then the blur wouldn't have been as pronounced.
When we got tired of doing that, we turned our lenses to the feluccas sailing the river. They're small lateen-rigged sailboats, and one of the iconic sites on the Nile. Since we'd already been doing a pan blur shot of the water taxies, I suggested a different blur photo. This time we tried zoom blurs. Again, you use slow shutter speeds (usually 1/2 to 1/8 second when hand-held), but this time instead of tracking (panning) with the subject, you zoom your lens as you shoot the photo. There are a few tips I can suggest to make this work best. First, keep your subject in the center of the frame. That's the only place that will have a chance of staying sharp. Second, I find starting zoomed in (tight) and zooming wider to work best, though others may disagre. And third, start your zooming BEFORE you press the shutter button. That way you'll add less blur when moving the lens (starting the twist is more movement than continuing it). This shot was done at 1/4 second at f/6.3.
Finally, there are times when you have plenty of light, but still want to have blur. We took small horse-drawn carriages from the river to one of the temples. It was a bright sunny day, but I wanted to emphasize the action of the horses running. To do that I needed to get the shutter speed as low as possible, which I started by taking theISO as low as possible (lower ISO's require more light to make the exposure). Then I dialed my aperture (using Aperture Priority) to its smallest setting. For this shot I was at 100 ISO at f/22, which allowed my shutter speed to go low, to 1/20 of a second. Then it was just a matter of tracking the horse (panning) while firing off a bunch of frames. After all, I just needed one good one.
I like to say that you can make pictures anywhere you have light - it's just a question of what you do with that light.