When Flash was introduced, it was for creating vector-based animation and basic interactive games. (Kind of like Shockwave but lighter.) It became very popular very quickly because it did lots of neat stuff with very small (vector-based) files and because the browser plugin itself was only a few hundred kilobytes at a time when most people were on dialup and most other plugins (like Shockwave and QuickTime) were several megabytes. Once you downloaded the plugin (just a few minutes) you could be watching neat little cartoons in seconds.
So lots of people are freaking the hell out and saying the iPad (in particular) will flop because it doesn't support Flash, but I think Flash is where HTML tables were just a few years ago. Tables were originally designed to hold tabular data, then people started using them for layout, and once HTML and CSS got a little better, pretty much everyone abandoned them and they're now only used for their original purpose: holding tabular data. So will it be with Flash: it was invented for vector animation, people started using it for everything, but now that other (better, more standard, more open) technologies have matured, it will fall back to being used for nothing more than it was originally designed for--animation and games.
* and, of course, Flash can be a basic "wrapper" around video, enabling you to play video on lots of platforms, but video standardization efforts are making good progress too.