If you use flash for things like navigation, make sure it does not take any additional time by the user if they want to get somewhere. I'd say most flash sites I've seen it takes time for a menu to drop down, or for the flash to load, or for links to appear, or whatever. Special animated features will be cool looking but if it takes longer to navigate, forget about it. If I can't quickly easily navigate a site, I leave. Flash navigation is probably the leading reason why I just get up and leave some websites. Don't get me wrong, it can be very effective and elegant if done properly, but most people do it wrong.
Clicking an HTML link is instant. If your flash isn't, you may want to reconsider. Also, if memory serves me correctly flash is generally much larger than HTML meaning it will take more bandwidth on your server. That may be a non-issue but I thought I'd point it out nonetheless. Finally, if you have a flash intro, make sure you have an easy to find skip button.
As one last note, average people who aren't all "in" to the computer and internet like we are (less competance) may prefer flash because it is "prettier" which makes them feel more comfortable. But then again they mught not have flash and they'll get a box asking them to get it, which might scare them away.
EDIT: Also, I don't think anyone has brought up a databased php site which can be made very nice. But it takes a lot more work.