Pets are a touchy subject with many people and may be a deal breaker if you don't allow them. The decision is, of course, up to you. However, here are some things to consider when it comes to allowing pets or not.
1. Certain Kinds Only. Many landlords will state that they will only allow certain kinds of animals in their apartment. For example, my apartment complex does not allow dogs at all, and it is up to the individual unit owner if they want to allow cats or not. However, according to the bylaws of the complex, each unit is only allowed a maximum of one cat each. Some landlords only allow an animal that can be kept in a tank, such as lizards, fish, or snakes. Weigh the benefits of each type of animal over what can go wrong and see what works best for you.
2. Pet Deposits. A good amount of landlords will only allow pets if the person pays an extra deposit. This may be a monthly fee or a larger lump sum at the beginning of each lease. This often covers the amount that steam cleaning would cost or maybe even a new carpet depending on the damage that the animals cause. This is a good way to offset any problems you may have with a resident's animal.
3. By Request Only. I personally have a cat and always ask if a landlord would accept a small pet even if there is no information given. Sometimes I would ask even if the pet policy says no but it has been listed for a while. My current apartment was listed as no pets, but after asking I got the okay from the landlord. He said that he would allow a pet if I already had it, so that's another option that you may want to explore.
Pets can be difficult to work around for many potential residents, but there are some options for you to reach some middle ground. Hopefully everyone will be able to walk away happy.