I've just recently started renting a property and used Zillow for applications as it includes both credit and background checks. The service is free for landlords (so the price is right). Applicants submit all their info through Zillow and pay the application fee of $29. As the landlord, you then get the application, a background check, and a full credit report with FICO score. You can set it up so that anyone can apply or restrict it to "by invitation only".
As an added bonus, Zillow also will accept rent payments. Again, the service is free for landlords. Tenants can pay electronically with credit card, debit card, or ECH bank transfer. If the tenant pays with credit or debit card, there is a fee involved that the tenant pays, though I'm not sure how much (I assume whatever the discount rate is plus some nominal amount so Zillow makes some profit.) ECH transfers via Zillow are free for the tenant.
ETA: Zillow Online Rent Payments