Updated for macOS Catalina
A bunch of people have emailed me about getting Hypercard stacks running under emulation. Here is a pretty easy guide to running a Hypercard stack on a recent Mac (eg. running Mavericks, Mountain Lion, etc):
Place the Hypercard stack you want to access somewhere within your user folder: eg. Documents, or Desktop.
Extract and open
hypercard.sheepvm. This should boot Mac OS 9.
On the Mac OS 9 desktop there should be a disk called "Unix". This is a virtual disk which actually lets you access files on your computer (eg. outside the emulator). Opening it is equivalent to opening your OS X
From there, navigate to your user folder (eg. your OS X username) and then to the folder you placed your Hypercard stack (in the first step).
Copy your Hypercard stack from the 'Unix' disk to somewhere on the OS 9 'Macintosh HD' disk.
Double-click the Hypercard stack in the location you placed it on the OS 9 'Macintosh HD' disk (or open it from within Hypercard).