“[…] Very softly, at seemingly random intervals, I hear a noise like a gunshot or a bomb/cannon going off. […]”

There are a few reasons you might hear something like that…

First, check in System Preferences, under Sound, and see what Alert Sound you have defined.

Second, check iChat’s own Sound Effects.  Especially the “Buddy becomes available/unavailable” sounds. When a buddy comes or goes, you hear the sound. To change it or turn it off, select iChat > Preferences > Alerts and Buddy Becomes Available/Unavailable.

If neither of these are the answer, how about leaving a comment…?