Remember that checkbox in the System Preferences (the Universal Access pane) called "Enable access for assistive devices?" If you enable it, any application will have access to the AX API, and vise versa: If you disable it, no application will be able to use the AX API functions. Among the AX API functions are capturing of text under the mouse pointer, capturing of keystrokes, etc
Theoretically, when enabled, this global option decreases your Mac's stability and robustness and creates a security hole accessible by key loggers, trojans, etc.
Although it's not as bad as it may sound, you would probably agree that it is better to err on the safe side.
What applications may need the AX API?
Don't enable this global option, use Trust.app instead to give access to the AX API only to your trusted applications.
To be able to access the AX API, newly added applications have to be restarted.
All your "trust settings" are saved between Mac OS X restarts.
If an application you have added to your trusted list crashes on start (in Mac OS X 10.5, see section 2 below), just remove it from the list, contact its developer with the link to this page.