I've purchased both Studio MX and Director MX from Macromedia, though I haven't even had a chance to take the shrinkwrap off Director yet.
In general, Flash has become the standard development application for multimedia stuff on the Web. Of course, you can also build self-contained, self-running Flash "programs" that can operate on their own (without Web connectivity). These are similar to "projectors" in Director terminology, which also run on their own. To further blur the line, Director files can also run on the Web via the Shockwave plug-in.
Both programs have their advantages and disadvantages. I have friends/colleagues who swear by Flash, and others who like Director better. If you're doing just basic, animated projects (that don't require a lot of database connectivity or other advanced features), Flash is a good choice. If you want more advanced controls and features, go with Director (which is often used to create entire SOFTWARE programs from scratch).
Then again, if you're looking mainly for funky type treatments/effects, check out SWiSH as an alternative: