No, most sites do not run Flash and as has been said, Adobe itself has abandoned mobile Flash development. Apple has always refused to support it because it's garbage that slows the phone down and sucks up battery life, this is the same reason Windows Phone doesn't support it. Android supports it because Google does not care about controlling the absolute quality of the end user experience the way Apple and Microsoft do.
Originally Posted by sut1576
Flash doesn't even work all that great on computers. Try running a bunch of flash apps on a laptop and watch it get hotter and hotter and the battery life drop. This is why some browsers even have plug-ins to disable Flash.
Adobe is finally accepting that Flash sucks and they are working on a whole new platform called Adobe AIR. They are probably going to let Flash linger on the desktop for a while yet because some developers are lazy and it's going to take forever to eradicate that garbage from the Internet, but AIR will probably replace Flash there too eventually.
So where it leaves us is, if web developers want their sites to be accessible to the ever increasing number of mobile users, they are going to have to walk away from Flash, or at the bare minimum, make alternate mobile sites that don't use it (MANY already do this) or develop smartphone apps to give the user a better experience than any website would.