Your question is a good one......but not easily answered because the regulations involving pet ownership varies from one home owners association to another.
The best way to access this information is to do so with the assistance of a real estate professional. There are a few communities that are "pet friendly" however, you are correct with your theory of the majority of condos not allowing any pets.
What these current search fields boil down to is that I would have to call every listing that reads Limits or With Approval to find out what the restrictions for having a pet would be. I think you can imagine the amount of time that would take. I have lobbied for YEARS to have the MLS change the pet fields to no avail.
A good rule of thumb to go by is that high rises will usually restrict dogs you can not carry. The pet rules for any other type of condo would have to be individually checked.
I can tell you that Lambiance, http://Lambiance.wordpress.com , in Pelican Bay, http://lambiance.wordpress.com/about-pelican-bay/ ,will allow one pet any size with no weight restriction. Covington Row at the Crescent in Pelican Bay will allow two pets less than 25 pounds.
Although some communities have restrictions and prohibitions, most do not and restrictions are an individual owner choice. I am assuming you are refering to 'domestic pets'.
If you would like to discuss this further with me, phone me directly at 239-560-0014.
Dennis Leffert, J.D.
Lic Real Estate Broker
Condo associations very typically will allow pets but control it by weight and number limitations. Single Family homes usually dont have these limitations.
Any other questions please feel free to contact me directly at 239-777-0408 or my website http://www.NaplesRealestateshop.com