This will depend on the Owner's or Property Manager's requirements.
We are a Management company, who doesn't check credit, simply for the reason that almost everybody who wants to rent has an issue with his/her credit. Specially the ones who lost their home in foreclosure.
We do a Criminal Background check and look for problems with previous Landlordsn (Evictions) to qualify our Tenants.
Use this argument when you talk to somebody about renting an appartment, it just makes sense.