Just to state some basic facts…
- Flash doesn’t work _everywhere_, unlike normal HTML. My computer runs a 64-bit OS without 32bit emulation, and Adobe has yet to provide a Flash player for any 64-bit platform.
- Flash requires a proprietary plugin.
- Flash does not let users change font sizes or contrast settings using personalized stylesheets.
- A lot of screenreaders and other accessibility tools does not work with Flash (some screenreaders does using a Windows-specific API).
- Flash is not indexable by all search engines. Some does index text in Flash files, but since there is no way to link to the subpage your query was found in, people can’t be redirected to the result, making the result useless for users.
- If a browser doesn’t support Flash, you get nothing unless the entire website is also saved in a standard compliant (also know as HTML) way. If a browser doesn’t support CSS, you will still get a readable website.
- Flash doesn’t not present my usual OS widgets (textfields, submit buttons and such) or use my OS settings for these (larger fontsizes, higher contrast and such).
- Flash is owned by a commercial entity and even though the format specification is open, it is not licensed for free use.
- Flash sites breaks the back button, a fundamental function that users are used to.
- There is no way to bookmark a subpage of most Flash-only sites.
- Flash doesn’t work in most alternative browser devices, like PDAs or Smart phones.
- Printing content from a Flash site is extremely difficult and most of the time comes out weird on paper, if at all.
Flash doesn’t provide a standard way of navigating without the mouse(tab navigation is possible by default).
Note: I’m not saying Flash should be banned from the net, I think there are numerous valid reasons to use Flash. But my opinion is that it should only be used for interactive multimedia which cannot be represented in HTML/CSS/JS in an easy way. Stuff like games, ads and (because of terrible object tag support in browsers) video playback. If you need to use Flash to have graphical menu buttons with mouseovers or display a logo in the header of your site you really should reconsider your profession. :)
Edit: Item 5 moderated, item 13 refuted.
Sidenote: Tadeusz Szewczyk at Fadtastic talks about the demise of Flash.
Edit: Item 4 moderated.