I love animals and agree that having a "no pets" policy cuts off a large pool of applicants. If you are in a renters' market, then it makes sense to allow them. But if the market if more balanced, having a no pets policy is easier to have and enforce. Pets bring with them a host of issues that add to a landlord's headaches. Large dogs do damage to property by digging, chewing, and clawing. There is daily poop that many tenants don't bother to pick up, leading to flies everywhere in the warmer months. They may bark incessantly when no one is home.
Cats are a little more gentle on the property, but can inflict major damage with their need to scratch. If no scratching posts are available, your kitchen cabinets and other furnishings become their target. If you get a cat who likes to mark his territory, good luck with getting rid of the urine smell.
For cats and dogs, the worst issue has to be FLEAS!!! As this thread confirms, once established, they are nearly impossible to eradicate due to their four-phase hatching cycle. In the worst cases, fleas will infest the entire house for weeks if not MONTHS. In multifamily units, they easily travel from one rental to the other.
Not worth the risk and hassle, in my opinion.