I suppose it really depends on where you live. Although writing a letter probably won't hurt. Here in Lausanne with the 0% empty-houses-rate (

am looking for one myself now) the agencies can do pretty much whatever they want, and they also appear to do that.
What you should send along is usually mentioned on the application form. Here it is at least an "extract des office du poursuite" (to prove you have ne debts in Switzerland), copies of 1 to 3 months of paychecks, copies of your passport and/or residence permit, sometimes a letter or contact details of a reference. (Preferably a swiss person imo, perhaps your boss?), and whatever else the agency can think of.
So far, the process seems pretty untransparent to me, and nobody seems able to tell me how it exactly works, or what the criteria are...
I have decided to play the I-miss-my-fiancee-and-really-need-a-place-to-allow-her-to-come-over card recently. Results are not in yet, though ;-)
Good hunting!