First of all, I advise you not to send your application by snail mail but fax it immediately or at the very least the next morning after visiting the flat. Attach all the relevant papers, state your income, Betreibungsregisterauskunft (debt statement), and references (very important!)
I applied for 8 appartments and got an affirmative call from 7. And I certainly wasn't the only applicant, there were at least 30-40 at every single visit I went to. All 7 or 8 of them called my boss (reference #1) and my previous landlord (reference #2), so they do indeed call before they chose you. All these appartments were publically listed on homegate.ch. Friends of mine (Swiss) searched for ages without success, but now that they adopted this advice they finally got an appartment, even as students. I suppose when they get a proper application by fax they just don't bother about the dozens or sometimes hundreds of letters coming in.