Flash is a plug-in (add-on) available on some 98% of all website browsers. As such it is the tool of choice for “special effects.”
I’m using “special effects” for the variety of multi-media and motion effects which can add a big chunk of pizzazz, interest, and attention-grabbing to a website.
These include:

audio (music or voiceover)
video (YouTube style)
walk-on-screen video
slideshows
morph effects
other animations
exotic menu effects

We love these kinds of effects but there’s always a balance between impingement (getting someone’s attention) and creating interest, versus being distracting or too over-the-top.
We almost always avoid “splash screens” (the introductory screen before you get to the home page).
In most cases sound or video should not start automatically but should be under the control of the visitor. If automatic they should be brief, and ideally the website should recognize and not offer it up on repeat visits.
Flash animations in many cases should play once through, then stop.
This is a matter of judgment and sometimes you don’t know until you’ve tried it where that balance is. And, of course, there’s no absolute answer for every visitor.