This term originiated in medevil england, where they threw trash in the streets and likewise. But one odd thing they did was throw dead animals on their roofs, thus they could rot and decompose without any smell. But once it rained really hard, the animals slid off their rooves thus giving u the expression, "its raining cats and dogs."
THis is NOT the real answer. It comes from a spoof essay called "Life in the 1500s" that has been circulating on the internet for several years. EVERYTHING in it is rubbish, but a frightening number of people believe it and snippets from it crop all over the place in "Did you know that?" - type threads.
You can read a good short debunking of the essay at http://www.snopes.com/language/phrases/1500.htm
and a more thorough one at http://historymedren.about.com/library/weekly/aa042202a.htm.
Anyone interested in the English language should read these, as it is full of fake word and phrase origins, e.g. "threshold", "dead ringer","raining cats and dogs", "wake", graveyard shift", "trench mouth" and so on. All untrue!