In Flash you can tween objects. This means you can set there start place, there finishing place and then let the computer do the rest. You can use masks, motion paths and good drawings skills to do this quite effectively and if you think about things carefully you can make things look exceptional. I have seen some truly fantastic work done with tweening, but I have also seen (And made myself) some really terrible stuff.
Because tweening is so quick and easy, there is a temptation to use it everywhere and you can do it so why not? Well, it is hard to make it look like it wasn't done with a computer. The trick is to and keep things as organic as possible by knowing what you can get away with. You can create a walk cycle within a symbol and tween it across a stage...there will generally be some slippage (Where the background moves on a different timing to the character or vice versa) but it is an effective and time saving technique. For things like rain, falling leaves, snow, wind or a shot with something flying through the air, you can't go wrong, but with character animation you are gunna have to have stylised content otherwise you'll end up with a robot.
Here are some effective uses of computer animation in some of my shots:
In this scene there is a lot of speed and action, it creates a lot of movement. But there is only one drawing. The computer moves the character about and the flashing lines are only on/off frames. The Japanese manga style background also helps to push the idea that things are moving so fast you can't see the background.
In this scene there is only one drawing again, but because in the previous scene we see the boy jump out from behind a log, we know the character is in the air. So when we see him enter above the tree line its OK and float on down towards the camera, we believe it because we know he's in the air. Add a bit perspective blur and have him crisp up as he comes into focus and add some sun shine flaring up the camera and you've got a great shot without having to make more than one drawing.
Computer animation does have its advantages. But you couldn't use it all the time. I have seen plenty of animations that just have a single drawing sliding in front of a detailed background...but it still looks like what it is and this style of animation earned the name 'radio with pictures' in the mid-sixties because budget cuts meant there was so little animation.