I agree that it also depends on who you're designing the site for.

Different types of designs attract different demographics. I actually think a hybrid site (css and flash) can get the job done very nicely.

There are some things to keep in mind though.

1. You should be at least a decent designer. Flash is all about the graphics. So if you lack in graphic design or getting your message across in graphics and text...hold off until you can. There is no CSS or HTML in Flash. So your job is purely graphics and layout. Then animation.

2. Don't use flash just for the sake of using. Make sure you have a clear idea in mind, and make sure your idea NEEDS flash. Once that is out of the way, make your idea come to life using the tools that are necessary for the job. Never use something just because it's "cool", because it's likely that your idea won't come off as cool if used for that reason.