I have hit a couple of sites that use flash but nothing that stopped me doing what I wanted. Probably the worst was Odean Cinemas, here in the UK. They use a flash app to let you select your seats. No flash and it pops up a message to that effect, but there is an HTML version, just the link is pretty well hidden. Other than that no issues really.
Oh and as a web developer who uses JW player (excellent flash movie player), I just heard they have an HTML 5 version in beta testing. Examples on their support site and they work great on the iPad. We'll be moving our clients to this version as soon as it is full release. (and no I don't work for Longtail, just a starving web developer who likes their product).