Under OS 9 you can assign the function keys at the top of most keyboards (F6 for example) to run scripts. Open the Keyboard control panel and click the “Function Keys…” button, then choose which function key you want to use and navigate to the script it will invoke.
There are several more versatile ways to attach a handy keyboard shortcut to a frequently used script. QuicKeys can launch anything, including AppleScripts and it can also create many other shortcuts all of which can be called by scripts.
In OS 9 and below, we had a cool alternative, Leonard Rosenthol’s invaluable OSA Menu which puts a configurable menu of scripts in your toolbar for easy access. It also allowed you to assign keyboard shortcuts to the items in that menu.