Flash isn’t supported on iOS, and Adobe just stopped supporting it on Android 4.1. Unless your website is such that it only makes sense on a desktop PC, you have to pay attention to the mobile market, and therefore you can’t ONLY use flash. If there’s something else that will do the job, that works both on the desktop and mobile, why would you use Flash at all?

That’s not to say that every use of Flash can be easily and directly replaced with other technologies, but you can build a really nice web site lots of ways. Flash used to be the most popular and well supported (lots and lots of folks had the Flash plugin installed), but there are other ways to do cool stuff now – they aren’t exactly the same, but they can make for a nice website and not necessarily need a plugin.

Most things Flash is/was used for can be done with HTML5 and Javascript – and unlike Flash, it will work on iOS devices.

Flash has a number of downsides:

• It is proprietary
• It doesn’t integrate well with the surrounding document structure
• It doesn’t come built into the browser
• It is mostly opaque to search engines, screen readers, and other non-desktop-browser user agents

Back in the days, Flash was the only viable way of doing what people do with it – animations, multimedia, interactive vector graphics, reliable fonts, etc. But today, we have modern browsers with much richer styling possibilities, a decent amount of standardization, fast Javascript engines, and APIs for vector graphics, sound and video, and even 3D graphics (although I wouldn’t consider this one quite ready for prime time yet) – almost all the reasons for using Flash are gone, but the downsides remain.