We own a condo that we rent out, but our rule is no pets. Even if we did allow pets, I would strongly consider other similar candidates that didn't have pets. If I did rent to someone with pets, I would add a monthly amount to the rent (I've seen many places add $100-250 per month) and I would take carpet cleaning out of your security deposit.
Sorry, but most landlords don't want to deal with pets. Like others have said - they can certainly be just fine, but then we have to deal with neighbors complaining about barking, damage (sometimes permanent) to the carpets, scratching, the pet being there for servicemen, etc.