Is there a program or such that I can use to "mute" other programs, such as Safari? That would prevent it from playing sounds from Flash sites and the like. Generally Safari shouldn't make sounds so I just want to cut it off for ever.
'Generally Safari shouldn't make sounds so I just want to cut it off for ever.', is not a valid statement. Generally, any current web browser (such as 'Safari', 'Camino', 'Firefox', 'Mozilla', 'iCab', 'OmniWeb', Opera', 'Shiira', etc.) supports a variety of graphic, sound, and video formats. One such video format being '.swf' files - also known as, 'Flash' files.
A web browser interrupts the HTML code of the visited web page. If a sound, graphic, or video file reference is embedded within a visited web page's HTML code, one will then experience such.
'Is there a program or such that I can use to "mute" other programs, such as Safari?' ... 'Is that possible?', yes and yes - it (the application you seek) is built in every MacOS X release. 'System Preferences' 'Sound' utility. Click on the 'mute' check box.