I agree with David's post, you can use HTML5 video... if you only want to display video. But HTML5 video is a far cry from an advanced Flash creation. It lacks the interactivity and customization of advanced Flash.
A Flash, "Best Practice" that has been around for a long time is to use some means of Flash detection and then provide alternate content for non-Flash platforms.
This is more or less the same principle as HTML5 video... provide multiple versions of a video and let the browser see if it can find a version that it can use, which may or may not display directly on your Web page (as opposed to opening a new window/tab).
swfobject is one method of Flash detection that has been around for a long time.
http://code.google.com/p/swfobject/
If you are heavily invested in your Flash creations and want to continue to use them, you can, just provide Flash detection and alternate content. That alternate content can be as simple or elaborate as you have time and effort to do.
Here is simple example of a Web page created using Flash and then providing alternate HTML content.
View the site in both Flash enabled and non-Flash device to compare (and view the alternate content).
http://www.ksowetsuits.com/
The alternate content version contains extensive HTML descriptive text content which not only is used as the alt content but is also indexed by search engines (disspelling the myth that Flash is always bad for SEO).
In the future, you might want to target more mobile devices and move away from Flash altogether, but for now, you can have the best of both worlds.
Best wishes,
Adninjastrator
