If they are truly past the point where I'd be seen carrying them, I trash them. If they are in wearable condition but I'm done with them, I give them to Goodwill.
I think it's important to make that distinction. A friend of mine once tried to donate a set of dishes to Goodwill, many of the plates chipped, and was told: "Poor people don't want your trash, lady." That comment has always stuck with me. If a bag is trash, it's trash and I should throw it away myself.
Vintage Leather, I appreciate your perpective. I have had some "accidents" that I think make a bag beyond use (huge ink stains, horrible mold, and a tragic mothball curse when I loaned a bag to my SIL) and would love to know if those things would make you get rid of a bag?