Flash is a great technology that allows you to do things that can not be done with regular HTML. However, there are significant disadvantages to having a Flash Site.
Search Engines can not read Flash Files. Therefore if you want your site to be listed on the search engines you should not use Flash.
Flash Sites are Huge. A very average Flash Site can approach 1 MB. If your customers are on dial-up they might be waiting 20 to 40 seconds for your site to download. Since most visitors will only wait 8 seconds they will probably just leave your site altogether.
You must click to Activate. Internet Explorer implemented this warning message a while ago. Your visitor must click on the Flash File once before any of the buttons will work. This can confuse people. There is a work around Javascript script. But with the next browser update, that will probably cease to work.
Flash has a fixed box. With HTML you can have some of your pages very long and others very short. With Flash everything must fit inside the movie screen.
The Scroll is Dead. To overcome the fixed sized box issue, Flash sites often have scroll bars and sliders. However these are often hard to grab. It is often just a design issue. The designer used the wrong anchor point or a small hit box.
There's no business like show off business. Often the whistles and bells incorporated into flash sites have no relevance to the business owner's business. It's more of a showcase for the frustrated film director that is designing the site.
It's very cool.
It looks neat.
Flash sites can give you a cutting edge look.
Protect your stuff. Flash files are hard (but not impossible) to steal. If you want to protect your photographs, graphics, etc., Flash is a good option.
Flash allows precise positioning. You can put your words and pictures exactly where you want them. Your visitor will see what you wanted them to see. This is often not the case with HTML. Although CSS allows for exact positioning there are still variations due to browser used, screen resolution and other issues.
You could use a Flash Site if you do not want to be listed on the search engines and ALL your customers have high speed connections.
Now I've been talking about Flash Sites which I obviously advise against. However,
Flash files can be used inside a regular web page. They are great for picture galleries and slide shows. They are also very effective for forms, calculators, banners, and games.
Flash can incorporate music, pictures, and words all into one file. Just be cognizant of your file size. Keep your music files short and highly compressed. Crop and reduce all your photos before you import them.
Flash is often a better choice than Javascript, Java Applets, or Animated GIFs for dynamic web elements.
Flash files are scalable similar to SVG. Flash sites without imported pictures or music can be extremely small.
You should decide whether to use Flash or not based on the goals of your web site. Is your goal to be the coolest kid in town or for your site to found?