As a web developer, I find them extremely annoying, cumbersome, and straight up stupid. I know, this sounds rather idiotic, avoiding these websites like the plague, but I can't stand them.
When I see Flash used for things like games, or videos, it's okay, but I really dislike websites made with it.
When you make a website using Flash, you have to be sure of a few things...
- The user has an up to date version of Flash
- The user has a fast enough internet connection to load your site fast enough
- And finally, you have to make sure your user isn't on a device that doesn't support Flash (iPhone/iPad, anyone?).
These are big things to worry about.
A decent alternative to this, would be using a mixture of HTML5 and CSS3 if you want to get all fancy.
With HTML5 and CSS3, there is no external file to load (unless you keep your CSS sheet in a separate file, which is almost instantly loaded), no pesky plugins to update (if your browser is up to date, but there is always fall back methods) and no worrying about things like a user's graphic card quality (hi-res flash = lag).
Now, I'm not saying kick Flash out of the picture all together, but leave it for the games, videos, and other such things.
Just my two cents on the subject of Flash for websites.