Asking prospective tenants to fill out written applications can protect you from lawsuits filed by irate applicants that you rejected as tenants.
For example, suppose you talk to six applicants before renting one of your units. You pick Applicant #3 because you feel he is most likely to reliably pay the rent. Two weeks later, you get a call from a lawyer representing Applicant #5, who claims she was discriminated against because she is African-American and a single mother. If you aren't willing to pay $10,000 to settle the matter, you'll promptly be sued in federal court for $50,000.
Because you have no written documentation explaining how you picked Applicant #3, your insurance carrier proposes to pay the rejected applicant $10,000. After all, the insurance company points out, it looks bad that you picked a white male with no children, especially since it turns out that the African-American single mother has a higher-paying job.
Had you been able to produce all the candidates' comprehensive written applications, their credit reports, and references from previous landlords, the result would likely have been different. You would have had good written documentation supporting why you picked Applicant #3 -- his credit history and job stability were far better than that of Applicant #5, who (despite her current good job) had recently declared bankruptcy and had poor references from previous landlords.
For more information, see Nolo's article Choosing Tenants: Avoid Fair Housing Complaints and Lawsuits.