The <embed>
tag is supported in all the major browsers. So the embed tag itself is supported, it's the content that the embed tag attempts to display that isn't supported.
You mention a swf file in your question. A lot of times a Javascript solution like SWFObject is used to figure out if Flash is available, and replace an element on the page with the Flash movie if flash is available. And if Flash isn't available, your alternate, or "Not supported" content would display instead.