Flash or no flash.
Motion is key on a website. You need it to be carefully planned out though, so that your visitor doesn't get whiplash trying to follow all the animated this and motion that, and not know where his/her eye should be going first.
However with motion, you also have to take into account the mobile factor. Smart phones don't... do...mobile. Mobile browsing only represents about 3% of the North American browsing market but it is a growing sector.
So if not flash, what's the alternative? Animated gifs are an older technology, however they can definitely accomplish the task.
Your visitor doesn't need flash installed on his computer and can view through a mobile browser.
The file size of the animation is a bit larger than a flash animation, and animated gifs won't allow the visitor to interact with the graphic.
Tomorrow, PC verses Mac viewing experiences.