Edit: In 8.2 Blizzard changed the way the client processes sounds.
The most recent uploaded file for 8.2 uses "I can't carry anymore," which uses Sound ID 540594 in the lua file.
If you prefer the old "Inventory is full" using Sound ID 540575, that is the second to last upload.

Bags get filled all the time, and if you have error sounds turned off, you don't ever hear the only error message that matters, "Inventory is full." And being that there are no error message addons that filter down this narrowly, therein lies the problem - and a simple solution.

Bagsfull is an audio alert when bags are full. That's it. Very slim file. In fact, it's shorter than the text in this description. The audio is the human female error message saying "Inventory is full" or "I can't carry anymore."

This addon especially helps when:

-Raiding and PVE so you won't miss out on loot

-Auctioning, especially if you are retrieving mass mail and are alt tabbed out

Why don't you just make a weakaura, you ask. Well, I made one that does just this but I have so many WA that if I'm on one of my many bank toons it would take forever to load. So I just use this.

Caveat: Seems to fire when reloading, logging, or zoning into an instance.