Flash is a very bad way to build websites. It’s not only about SEO. It’s about usability. For the same reasons that mature developers don’t use “fly-out” or “drop-down” menus, you shouldn’t use Flash because it requires you to do one of two things. You can either alienate the growing minority of users using alternative user agents or you can “sniff” to find out what the user is using and deliver one site if the user is using Firefox on a Mac and another site if the user is browsing using Internet Explorer on Windows Mobile. Either option is a bad decision.
Properly designed websites keep usability in mind for 100% of possible users. They’re made with semantically valid XHTML and CSS. They don’t start animation or sound without the user clicking somewhere to request it. They don’t require the user to download something special like Flash or Java. They load faster because of the lighter page weight caused by separating the markup (XHTML) from the layout (CSS). They have a good navigational structure that doesn’t rely on drop-down or fly-out menus. They can be browsed effectively with a text-based browser or screen reader. They are very well-indexed on search engines because they’re so accessible.
Flash does have one redeeming quality. It is the current, defacto standard for video distribution. Until Silverlight gets out of diapers, it appears we’re stuck with Adobe’s pile of steam for now.