actually i think rental prices will rise in the short term because of all of these people leaving homes and becoming renters. Yes, the empty home will become a rental at some point, but there will be a significant lag. The longer the lag between the homeowner leaving the house and the house becoming a rental, the more pressure on the rental price. It may take time for a bank to find a buyer/investor who will purchase the property and bring it to use. Combine that with the possible difficulty of obtaining financing for the property, and I see at least some pressure on rental prices.
Bottom line, these thousands and thousands of foreclosures are not going to be turned into rentals overnight (which is the scenario where the foreclosures would directly lower the price of renting).
The smart (and more experienced) landlords do run a credit check. In the beginning they may not want to rent to those who have a bankruptcy or some sort of financial problem, but will have to make considerations for it as time goes on. AS long as the tenant can document his income, it shouldn’t be a big problem, though.