SheepShaver is Mac OS run time environment, with a built in PowerPC emulator. As well as being available for OS X, it can also be run on Linux and Windows.
With SheepShaver you can set up a virtual environment to run your old OS 9 (and earlier) applications. Have a look at this Emaculation article on how to set up SheepShaver on OS X.
You may also want to do a Google search for Chubby Bunny, which is already preinstalled and preconfigured SheepShaver running OS 9, ready to be used out of the box on your OS X.
I have found SheepShaver to be generally stable, and was able to install and use applications on it. If you have a need to run some of your old Mac software, but don’t have PowerPC based Mac anymore, this might be useful.