Then, maybe you can get them out for criminal behavior?

., is he a tenant with rights you need to evict or a criminal trespasser that can be removed by police?)

You always need to run a background check on the individual applying as well, especially a criminal background check.

Figure out your criteria (accept pets, how many people, criminal OK, etc), how you are going to process applications (on-line service, fax in their application form, self serve), etc.As far as renting another place, it shouldn't hurt you - you have proven yourself financially responsible, that you are able to take care of minor maintenance issues, and probably have more realistic expectations.  

Screen for everything - credit, criminal, evictions, check all references. 

To follow up on the SmartMove check---it finally came back complete and she has perfect credit, no criminal record and no eviction history. 

I see small chinks in the landlord dam...for instance landlords supposed to disregard criminal records and today as a real life example I had an offer on a house and they potential buyers had $100 down !

Did you do any background, criminal, job verification?

I would still run a credit/criminal check to make sure they check out. 

Not a lawyer, no legal advice, but HUD just released guidelines of a sort explaining that criminal backgrounds should be judged on a case by case basis, not a standard, no criminal record clause.