Director can be used but usually isn't unless you're putting up a shockwave application, whether it be a game, multimedia player, chat, or whatever. Flash would be a better route if you need animation due to the smaller file ....really just depends what you need on the site. I built a chat app in Director and used that on my site for awhile but ended up taking it down because I couldn't quite customize it the way I wanted...my mediocre lingo skills, I'm afraid. Figure out what you need on the site and go from there. Flash is very robust now as far as dynamically loading files and whatnot...takes a bit of actionscripting know-how but worth it.
"Terminat Bora Diem, Terminal Auctor opus."