This article is from the Cats and the Outside World FAQ, posted to rec.pets.cats newsgroup. Maintained by Cindy Tittle Moore with numerous contributions by others.
A number of landlords initially say "no pets" but change their minds when assured that the cat was well-behaved and assured of an extra damage deposit if necessary.
Also, it seems like many landlords are more likely to approve of a cat if you make it a condition of signing the lease, rather than if you ask if it's OK to get one after you've already moved in, or if you try to sneak one in without asking.
Try to prove that you are a responsible owner (photos of last house, references, vet records, etc.) to help win your case.
For more ideas and tips, look up Dog Fancy, Volume 22, No. 8, August 1991, "Breaking Barriers: How to find an apartment that allows dogs," by Amanda Wray. The tips can be easily adapted for cat owners.
 
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